# Posts Tagged mass function

## Recent Postings from mass function

### 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.

### 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.

### Cosmic history of integrated galactic stellar initial mass function : a simulation study

Theoretical as well as observational studies suggest that the stellar initial mass function (IMF) might become top heavy with increasing redshift. Embedded cluster mass function is a power law having index $\beta$, whose value still remains controversial. In the present work, we investigate the effect of evolving IMF and varying indices of $\beta$ for the integrated galactic initial mass function, in relation to several measures of star formation rates of galaxies at various redshifts by random simulation. The resulting IGIMF is segmented power law at various redshifts having slopes $\alpha_{1,IGIMF}$ and $\alpha_{2,IGIMF}$ with a turnover at a characteristic mass $m_{c^{‘}}$. These differ from the stellar initial mass functions with slopes $\alpha_{1,IMF}$, $\alpha_{2,IMF}$, and characteristic masses $m_{c}$ for different values of redshift z, $\beta$, minimum and maximum masses of the embedded clusters.

### AGN evolution from a galaxy evolution viewpoint

We explore the connections between the evolving galaxy and AGN populations. We present a simple phenomenological model that links the evolving galaxy mass function and the evolving quasar luminosity function, motivated by similarities between the two, which makes specific and testable predictions for the distribution of host galaxy masses for AGN of different luminosities. We show that the phi$^{*}$ normalisations of the galaxy mass function and the AGN luminosity function closely track each other over a wide range of redshifts, implying a constant "duty cycle" of AGN activity. The strong redshift evolution in the AGN break luminosity $L^*$ is produced by either an evolution in the distribution of Eddington rations, or in the $m_{bh}/m_{*}$ mass ratio, or both. An evolving $m_{bh}/m_{*}$ ratio, such that it is ten times higher at $z \sim 2$ (i.e. roughly following $(1+z)^{2}$), reproduces the observed distribution of SDSS quasars in the ($m_{bh},L$) plane and accounts for the apparent "sub-Eddington boundary" without new physics and also satisfactorily reproduces the local relations which connect the black hole population with the host galaxies for both quenched and star-forming galaxies. The model produces the appearance of "downsizing" without any mass-dependence in the evolution of black hole growth rates (Eddington ratios) and enables a quantitative assessment of the strong biasses present in luminosity-selected AGN samples. The constant duty cycle is only consistent with the idea that AGN trigger the quenching of star-formation in galaxies if the lifetime of the AGN phase satisfies a particular mass and redshift dependence.

### Low-End Mass Function of the Arches Cluster

The initial mass function (IMF) of the Arches cluster, which was formed a few million years ago in the harsh environment of the Galactic center (GC), has long been a target of interest to those who study the GC and the theory of star formation. The distinct star-forming conditions in the GC might have caused the cluster to have a shallower slope or an elevated lower mass cutoff in its IMF. But its mass function has been revealed only down to 1-2 Msun (the lower limit of resolved stars), and the low- end mass function of the Arches is still unknown. To estimate the unresolved part of the Arches mass function, we have devised a novel photometric method that involves the histogram of pixel intensities in the observed image, which contains information on the unresolved, faint stars. By comparing the pixel intensity histograms (PIHs) of numerous artificial images constructed from model IMFs with the observed PIH, we find that the best-fit model IMF for the Arches cluster has a cutoff mass less than or similar to 0.1 Msun and a shape very close to that of the Kroupa MF. Our findings imply that the IMF of the Arches cluster is similar to those found in the Galactic disk.

### Deconstructing the Galaxy Stellar Mass Function with UKIDSS and CANDELS: the Impact of Colour, Structure and Environment

We combine photometry from the UDS, and CANDELS UDS and CANDELS GOODS-S surveys to construct the galaxy stellar mass function probing both the low and high mass end accurately in the redshift range 0.3<z<3. The advantages of using a homogeneous concatenation of these datasets include meaningful measures of environment in the UDS, due to its large area (0.88 deg^2), and the high resolution deep imaging in CANDELS (H_160 > 26.0), affording us robust measures of structural parameters. We construct stellar mass functions for the entire sample as parameterised by the Schechter function, and find that there is a decline in the values of phi and of alpha with higher redshifts, and a nearly constant M* up to z~3. We divide the galaxy stellar mass function by colour, structure, and environment and explore the links between environmental over-density, morphology, and the quenching of star formation. We find that a double Schechter function describes galaxies with high Sersic index (n>2.5), similar to galaxies which are red or passive. The low-mass end of the n>2.5 stellar mass function is dominated by blue galaxies, whereas the high-mass end is dominated by red galaxies. This hints that possible links between morphological evolution and star formation quenching are only present in high-mass galaxies. This is turn suggests that there are strong mass dependent quenching mechanisms. In addition, we find that the number density of high mass systems is elevated in dense environments, suggesting that an environmental process is building up massive galaxies quicker in over densities than in lower densities.

### Mapping the core mass function to the initial mass function

It has been shown that fragmentation within self-gravitating, turbulent molecular clouds ("turbulent fragmentation") can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently-developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the IMF. First, a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity. We predict the IMF slope (-2.3) is slightly steeper then the CMF slope (-2.1), owing to the slower collapse and easier fragmentation of large cores. Second, a turnover mass, which is set by a combination of the CMF turnover mass (a couple solar masses, determined by the `sonic scale’ of galactic turbulence, and so weakly dependent on galaxy properties), and the equation of state (EOS). A "soft" EOS with polytropic index $\gamma<1.0$ predicts that the IMF slope becomes "shallow" below the sonic scale, but fails to produce the full turnover observed. An EOS which becomes "stiff" at sufficiently low surface densities $\Sigma_{\rm gas} \sim 5000\,M_{\odot}\,{\rm pc^{-2}}$, and/or models where each collapsing core is able to heat and effectively stiffen the EOS of a modest mass ($\sim 0.02\,M_{\odot}$) of surrounding gas, are able to reproduce the observed turnover. Such features are likely a consequence of more detailed chemistry and radiative feedback.

### Constraining the primordial initial mass function with stellar archaeology

We present a new near-field cosmological probe of the initial mass function (IMF) of the first stars. Specifically, we constrain the lower-mass limit of the Population III (Pop III) IMF with the total number of stars in large, unbiased surveys of the Milky Way bulge and halo. We model the early star formation history in a Milky-Way like halo with a semi-analytic approach, based on Monte-Carlo sampling of dark matter merger trees, combined with a treatment of the most important feedback mechanisms, such as stellar radiation and metal enrichment. Assuming a logarithmically flat Pop III IMF and varying its low mass limit, we derive the number of expected survivors of these first stars, using them to estimate the probability to detect any such Pop III fossil in stellar archaeological surveys. Our model parameters are calibrated with existing empirical constraints, such as the optical depth to Thomson scattering. Following our analysis, the most promising region to find possible Pop III survivors is the stellar halo of the Milky Way, which is the best target for future surveys. We find that if no genuine Pop III survivor is detected in a sample size, of $4 \times 10^6$ ($2 \times 10^7$) halo stars with well-controlled selection effects, then we can exclude the hypothesis that the primordial IMF extended down below $0.8 M_\odot$ at a confidence level of 68% (99%). With the sample size of the Hamburg/ESO survey, we can tentatively exclude Pop III stars with masses below $0.65 M_\odot$ with a confidence level of 95%, although this is subject to significant uncertainties. To fully harness the potential of our approach, future large surveys are needed that employ uniform, unbiased selection strategies for high-resolution spectroscopic follow-up.

### Reddening, Distance, and Stellar Content of the Young Open Cluster Westerlund 2

We present deep $UBVI_C$ photometric data of the young open cluster Westerlund 2. An abnormal reddening law of $R_{V,cl}=4.14\pm0.08$ was found for the highly reddened early-type members ($E(B-V)\geq 1.45$), whereas a fairly normal reddening law of $R_{V,fg}=3.33\pm0.03$ was confirmed for the foreground early-type stars ($E(B-V)_{fg}<1.05$). The distance modulus was determined from zero-age main-sequence (ZAMS) fitting to the reddening-corrected colour-magnitude diagram of the early-type members to be $V_0-M_V=13.9\pm0.14$ (random error) $_{-0.1}^{+0.4}$ (the upper limit of systematic error) mag ($d = 6.0 \pm 0.4 _{-0.3}^{+1.2}$ kpc). To obtain the initial mass function, pre-main-sequence (PMS) stars were selected by identifying the optical counterparts of Chandra X-ray sources and mid-infrared emission stars from the Spitzer GLIMPSE source catalog. The initial mass function shows a shallow slope of $\Gamma=-1.1 \pm 0.1$ down to $\log m = 0.7$. The total mass of Westerlund 2 is estimated to be at least 7,400 $M_{\odot}$. The age of Westerlund 2 from the main-sequence turn-on and PMS stars is estimated to be $\lesssim$ 1.5 Myr. We confirmed the existence of a clump of PMS stars located $\sim1$ arcmin north of the core of Westerlund 2, but we could not find any clear evidence for an age difference between the core and the northern clump.

### Rates of Stellar Tidal Disruption as Probes of the Supermassive Black Hole Mass Function

Rates of stellar tidal disruption events (TDEs) by supermassive black holes (SMBHs) due to two-body relaxation are calculated using a large galaxy sample (N ~ 200) in order to explore the sensitivity of the TDE rates to observational uncertainties, such as the parametrization of galaxy light profiles and the stellar mass function. The largest uncertainty arises due to the poorly constrained occupation fraction of SMBHs in low-mass galaxies, which otherwise dominate the total TDE rate. The detection rate of TDE flares by optical surveys is calculated as a function of SMBH mass and other observables for several physically-motivated models of TDE emission. We also quantify the fraction of galaxies that produce deeply penetrating disruption events. If the majority of the detected events are characterized by super-Eddington luminosities (such as disk winds, or synchrotron radiation from an off-axis relativistic jet), then the measured SMBH mass distribution will tightly constrain the low-end SMBH occupation fraction. If Eddington-limited emission channels dominate, however, then the occupation fraction sensitivity is much less pronounced in a flux-limited survey (although still present in a volume-complete event sample). The SMBH mass distribution of the current sample of TDEs, though highly inhomogeneous and encumbered by selection effects, already suggests that Eddington-limited emission channels dominate.

### The connection between the UV colour of early type galaxies and the stellar initial mass function revisited

We extend our initial study of the connection between the UV colour of galaxies and both the inferred stellar mass-to-light ratio, $\Upsilon_*$, and a mass-to-light ratio referenced to Salpeter initial mass function (IMF) models of the same age and metallicity, $\Upsilon_*/\Upsilon_{Sal}$, using new UV magnitude measurements for a much larger sample of early-type galaxies, ETGs, with dynamically determined mass-to-light ratios. We confirm the principal empirical finding of our first study, a strong correlation between the GALEX FUV-NUV colour and $\Upsilon_*$. We show that this finding is not the result of spectral distortions limited to a single passband (eg. metallicity-dependent line-blanketing in the NUV band), or of the analysis methodology used to measure $\Upsilon_*$, or of the inclusion or exclusion of the correction for stellar population effects as accounted for using $\Upsilon_*/\Upsilon_{Sal}$. The sense of the correlation is that galaxies with larger $\Upsilon_*$, or larger $\Upsilon_*/\Upsilon_{Sal}$, are bluer in the UV. We conjecture that differences in the low mass end of the stellar initial mass function, IMF, are related to the nature of the extreme horizontal branch stars generally responsible for the UV flux in ETGs. If so, then UV color can be used to identify ETGs with particular IMF properties and to estimate $\Upsilon_*$. We also demonstrate that UV colour can be used to decrease the scatter about the Fundamental Plane and Manifold, and to select peculiar galaxies for follow-up with which to further explore the cause of variations in $\Upsilon_*$ and UV colour.

### Chemical evolution of the bulge of M31: predictions about abundance ratios

We aim at reproducing the chemical evolution of the bulge of M31 by means of a detailed chemical evolution model, including radial gas flows coming from the disk. We study the impact of the initial mass function, the star formation rate and the time scale for bulge formation on the metallicity distribution function of stars. We compute several models of chemical evolution using the metallicity distribution of dwarf stars as an observational constraint for the bulge of M31. Then, by means of the model which best reproduces the metallicity distribution function, we predict the [X/Fe] vs. [Fe/H] relations for several chemical elements (O, Mg, Si, Ca, C, N). Our best model for the bulge of M31 is obtained by means of a robust statistical method and assumes a Salpeter initial mass function, a Schmidt-Kennicutt law for star formation with an exponent k=1.5, an efficiency of star formation of $\sim 15\pm 0.27\, Gyr^{-1}$, and an infall timescale of $\sim 0.10\pm 0.03$Gyr. Our results suggest that the bulge of M31 formed very quickly by means of an intense star formation rate and an initial mass function flatter than in the solar vicinity but similar to that inferred for the Milky Way bulge. The [$\alpha$/Fe] ratios in the stars of the bulge of M31 should be high for most of the [Fe/H] range, as is observed in the Milky Way bulge. These predictions await future data to be proven.

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

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 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.

### 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 in this context. 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 in this context. 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.

### Galaxy Cosmological Mass Function [Replacement]

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.

### Galaxy Cosmological Mass Function [Replacement]

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 [Replacement]

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. 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.

### 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 [Replacement]

Our current understanding of the stellar initial mass function and massive star evolution suggests that young globular clusters may have formed hundreds to thousands of stellar-mass black holes, the remnants of stars with initial masses from $\sim 20 – 100\, M_\odot$. Birth kicks from supernova explosions may eject some black holes from their birth clusters, but most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of globular clusters containing large numbers of stellar black holes. We describe numerical results for 42 models, covering a range of realistic initial conditions, including up to $1.6\times10^6$ stars. In almost all models we find that significant numbers of black holes (up to $\sim10^3$) are retained all the way to the present. This is in contrast to previous theoretical expectations that most black holes should be ejected dynamically within a few Gyr. The main reason for this difference is that core collapse driven by black holes (through the Spitzer "mass segregation instability") is easily reverted through three-body processes, and involves only a small number of the most massive black holes, while lower-mass black holes remain well-mixed with ordinary stars far from the central cusp. Thus the rapid segregation of stellar black holes does not lead to a long-term physical separation of most black holes into a dynamically decoupled inner core, as often assumed previously. Combined with the recent detections of several black hole X-ray binary candidates in Galactic globular clusters, our results suggest that stellar black holes could still be present in large numbers in many globular clusters today, and that they may play a significant role in shaping the long-term dynamical evolution and the present-day dynamical structure of many clusters.

### 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 [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.

### 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.

### 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.

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