# Posts Tagged mass function

## Recent Postings from mass function

### 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 [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.

### 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

### Analytical Studies of NGC 2571, NGC 6802, Koposov 53 and Be 89

Astrophysical parameters (age, reddening, distance, radius, luminosity function, mass function, total mass, relaxation time and mass segregation) have been estimated for open clusters NGC 2571, NGC 6802, Koposov 53 and Be 89 by using the Two Micron All Sky Survey (2MASS) photometry. We analyse the color-magnitude diagrams and stellar radial density profiles. We have found that NGC 2571 is the youngest one having young main sequence stars while Be 89 is the oldest cluster.

### Characterising superclusters with the galaxy cluster distribution

Superclusters are the largest, observed matter density structures in the Universe. Recently Chon et al.(2013) presented the first supercluster catalogue constructed with a well-defined selection function based on the X-ray flux-limited cluster survey, REFLEX II. For the construction of the sample we proposed a concept to find the large objects with a minimum overdensity such that most of their mass will collapse in the future. The main goal of the paper is to provide support for our concept using simulations that we can, on the basis of our observational sample of X-ray clusters, construct a supercluster sample defined by a certain minimum overdensity, and to test how superclusters trace the underlying dark matter distribution. Our results confirm that an overdensity in the number of clusters is tightly correlated with an overdensity of the dark matter distribution. This enables us to define superclusters such that most of the mass will collapse in the future and to get first-order mass estimates of superclusters on the basis of the properties of the member clusters. We also show that in this context the ratio of the cluster number density and dark matter mass density is consistent with the theoretically expected cluster bias. Our previous work provided evidence that superclusters are a special environment for density structures of the dark matter to grow differently from the field as characterised by the X-ray luminosity function. Here we confirm for the first time that this originates from a top-heavy mass function at high statistical significance provided by a Kolmogorov-Smirnov test. We also find in close agreement with observations that the superclusters occupy only a small volume of few percent while they contain more than half of the clusters in the present day Universe.

### Halo abundances within the cosmic web

We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of cosmological theory, allowing mass-dependent biasing to be understood via the peak-background split. On the assumption of a Gaussian density field, this analysis can be extended to ask how the mass function depends on the geometrical environment: clusters, filaments, sheets and voids, as classified via the tidal tensor (the Hessian matrix of the gravitational potential). In linear theory, the problem can be solved exactly, and the result is attractively simple: the conditional mass function has no explicit dependence on the local tidal field, and is a function only of the local density on the filtering scale used to define the tidal tensor. There is nevertheless a strong implicit predicted dependence on geometrical environment, because the local density couples statistically to the derivatives of the potential. We compute the predictions of this model and study the limits of their validity by comparing them to results deduced empirically from N-body simulations. For sufficiently large filtering sizes, the agreement is good; but there are deviations from the Gaussian prediction at high nonlinearities. We discuss how to obtain improved predictions in this regime, using the `effective-universe’ approach.

### Decoding the X-ray Properties of Pre-Reionization Era Sources

Evolution in the X-ray luminosity — star formation rate ($L_X$-SFR) relation could provide the first evidence of a top-heavy stellar initial mass function in the early universe, as the abundance of high-mass stars and binary systems are both expected to increase with decreasing metallicity. The sky-averaged (global) 21-cm signal has the potential to test this prediction via constraints on the thermal history of the intergalactic medium, since X-rays can most easily escape galaxies and heat gas on large scales. A significant complication in the interpretation of upcoming 21-cm measurements is the unknown spectrum of accreting black holes at high-$z$, which depends on the mass of accreting objects and poorly constrained processes such as how accretion disk photons are processed by the disk atmosphere and host galaxy interstellar medium. Using a novel approach to solving the cosmological radiative transfer equation (RTE), we show that reasonable changes in the characteristic BH mass affects the amplitude of the 21-cm signal’s minimum at the $\sim 10-20$ mK level — comparable to errors induced by commonly used approximations to the RTE — while modifications to the intrinsic disk spectrum due to Compton scattering (bound-free absorption) can shift the position of the minimum of the global signal by $\Delta z \approx 0.5$ ($\Delta z \approx 2$), and modify its amplitude by up to $\approx 10$ mK ($\approx 50$ mK) for a given accretion history. Such deviations are larger than the uncertainties expected of current global 21-cm signal extraction algorithms, and could easily be confused with evolution in the $L_X$-SFR relation.

### Effects of shear and rotation on the spherical collapse model for clustering dark energy

In the framework of the spherical collapse model we study the influence of shear and rotation terms for dark matter fluid in clustering dark energy models. We evaluate, for different equations of state, the effects of these two terms on $\delta_{\rm c}$, and on $\Delta_{\rm V}$. The evaluation of the effects by the two non-linear terms on the linear overdensity threshold allows us to infer the modifications occurring on the mass function. Since there is an ambiguity in the definition of the halo mass in the case of clustering dark energy, we consider two different situations: the first is the classical one where the mass appearing in the expression for the mass function is the mass of the dark matter halo only, while the second one, more speculative, is given by the sum of the mass of the dark matter and dark energy fluid component. As previously found for the case in which dark energy effects are only at the background level, the spherical collapse model becomes mass dependant (in analogy with the ellipsoidal collapse model) and the two additional terms oppose to the collapse of the perturbations, especially on galactic scales, with respect to the spherical non-rotating model, while on clusters scales the effects of shear and rotation become negligible. The values for $\delta_{\rm c}$ and $\Delta_{\rm V}$ are therefore in general higher than the standard spherical model. Regarding the effects of the additional non-linear terms on the mass function, we concentrate on the number density of halos, i.e. the number of objects above a given mass at a fixed epoch. As expected, major differences appear at high masses and redshifts. In particular, quintessence (phantom) models predict more (less) objects with respect to the $\Lambda$CDM model and the mass correction due to the contribution of the dark energy component, has a negligible effect on the overall number of structures.

### Is the evidence for a variable initial mass function from ATLAS3D robust?

The ATLAS3D Survey has reported strong evidence for a non-universal stellar initial mass function (IMF) and for a trend of the IMF with the effective stellar velocity dispersion of early type galaxies (ETGs) (Cappellari et al. 2012). The ATLAS3D Survey consists of detailed Integral Field Spectroscopy of 260 ETGs closer than 42 Mpc. Cappellari et al. infer the IMF by comparing mass measurements derived from fitting the kinematic data with measurements derived from fitting the spectral energy distribution. Here we investigate possible systematic errors and biases that could affect their conclusions. We show that part of the reported trend between IMF and velocity dispersion is caused by a selection effect on H\b{eta} absorption. Apart from an IMF trend with velocity dispersion, we also find an IMF trend with distance, but no correlation between nearest neighbour ETGs as would be expected if the dependence on distance would reflect an environmental dependence. Part of the IMF trend with velocity dispersion can be traced back to colour-dependent calibration issues with the surface brightness fluctuation distances of Tonry et al. (2001) and Mei et al. (2007). There is no IMF-dispersion trend for galaxies with distances larger than 25 Mpc. The ATLAS3D Survey appears to be incomplete for masses lower than 10^10.3 solar masses. Restricting the analysis to the kinematic mass range M > 10^10.3 solar masses completely removes the IMF-dispersion trend. Our findings strongly suggest that some of the trends between IMF and galaxy properties reported by ATLAS3D are unphysical and caused by systematics.

### Reversal of Fortune: Increased Star Formation Efficiencies in the Early Histories of Dwarf Galaxies?

On dwarf galaxy scales, the different shapes of the galaxy stellar mass function and the dark halo mass function require a star-formation efficiency (SFE) in these systems that is currently more than 1 dex lower than that of Milky Way-size halos. Here, we argue that this trend may actually be reversed at high redshift. Specifically, by combining the resolved star-formation histories of nearby isolated dwarfs with the simulated mass-growth rates of dark matter halos, we show that the assembly of these systems occurs in two phases: (1) an early, fast halo accretion phase with a rapidly deepening potential well, characterized by a high SFE; and (2) a late slow halo accretion phase where, perhaps as a consequence of reionization, the SFE is low. Nearby dwarfs have more old stars than predicted by assuming a constant or decreasing SFE with redshift, a behavior that appears to deviate qualitatively from the trends seen amongst more massive systems. Taken at face value, the data suggest that, at sufficiently early epochs, dwarf galaxy halos above the atomic cooling mass limit can be among the most efficient sites of star formation in the universe.

### Reversal of Fortune: Increased Star Formation Efficiencies in the Early Histories of Dwarf Galaxies? [Replacement]

On dwarf galaxy scales, the different shapes of the galaxy stellar mass function and the dark halo mass function require a star-formation efficiency (SFE) in these systems that is currently more than 1 dex lower than that of Milky Way-size halos. Here, we argue that this trend may actually be reversed at high redshift. Specifically, by combining the resolved star-formation histories of nearby isolated dwarfs with the simulated mass-growth rates of dark matter halos, we show that the assembly of these systems occurs in two phases: (1) an early, fast halo accretion phase with a rapidly deepening potential well, characterized by a high SFE; and (2) a late slow halo accretion phase where, perhaps as a consequence of reionization, the SFE is low. Nearby dwarfs have more old stars than predicted by assuming a constant or decreasing SFE with redshift, a behavior that appears to deviate qualitatively from the trends seen amongst more massive systems. Taken at face value, the data suggest that, at sufficiently early epochs, dwarf galaxy halos above the atomic cooling mass limit can be among the most efficient sites of star formation in the universe.

### The Black Hole Mass Function Derived from Local Spiral Galaxies [Replacement]

We present our determination of the nuclear supermassive black hole (SMBH) mass function for spiral galaxies in the Local Universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the Southern Hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of SMBH evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of SMBHs since the epoch of maximum quasar activity. A luminosity distance $\leq$ 25.4 $Mpc$ and an absolute B-band magnitude $\leq$ -19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time $\leq$ 82.1 $h_{67.77}^{-1}$ $Myr$ and contained within a comoving volume of 3.37 $\times$ $10^4$ $h_{67.77}^{-3}$ $Mpc^3$. We estimate the density of SMBHs residing in spiral galaxies in the Local Universe is $5.54_{-2.73}^{+6.55}$ $\times$ $10^4$ $h_{67.77}^3$ $M_{\odot}$ $Mpc^{-3}$. Thus, our derived cosmological SMBH mass density for spiral galaxies is $\Omega_{BH} = 4.35_{-2.15}^{+5.14}$ $\times$ $10^{-7}$ $h_{67.77}$.

### The Black Hole Mass Function Derived from Local Spiral Galaxies

We present our determination of the nuclear supermassive black hole (SMBH) mass function for spiral galaxies in the Local Universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the Southern Hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of SMBH evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of SMBHs since the epoch of maximum quasar activity. A luminosity distance $\leq$ 25.4 $Mpc$ and an absolute B-band magnitude $\leq$ -19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time $\leq$ 82.1 $h_{67.77}^{-1}$ $Myr$ and contained within a comoving volume of 3.37 $\times$ $10^4$ $h_{67.77}^{-3}$ $Mpc^3$. We estimate the density of SMBHs residing in spiral galaxies in the Local Universe is $5.54_{-2.73}^{+6.55}$ $\times$ $10^4$ $h_{67.77}^3$ $M_{\odot}$ $Mpc^{-3}$. Thus, our derived cosmological SMBH mass density for spiral galaxies is $\Omega_{BH} = 4.35_{-2.15}^{+5.14}$ $\times$ $10^{-7}$ $h_{67.77}$.

### Building a Predictive Model of Galaxy Formation - I: Phenomenological Model Constrained to the $z=0$ Stellar Mass Function

We constrain a highly simplified semi-analytic model of galaxy formation using the $z\approx 0$ stellar mass function of galaxies. Particular attention is paid to assessing the role of random and systematic errors in the determination of stellar masses, to systematic uncertainties in the model, and to correlations between bins in the measured and modeled stellar mass functions, in order to construct a realistic likelihood function. We derive constraints on model parameters and explore which aspects of the observational data constrain particular parameter combinations. We find that our model, once constrained, provides a remarkable match to the measured evolution of the stellar mass function to $z=1$, although fails dramatically to match the local galaxy HI mass function. Several "nuisance parameters" contribute significantly to uncertainties in model predictions. In particular, systematic errors in stellar mass estimate are the dominant source of uncertainty in model predictions at $z\approx 1$, with additional, non-negligble contributions arising from systematic uncertainties in halo mass functions and the residual uncertainties in cosmological parameters. Ignoring any of these sources of uncertainties could lead to viable models being erroneously ruled out. Additionally, we demonstrate that ignoring the significant covariance between bins the observed stellar mass function leads to significant biases in the constraints derived on model parameters. Careful treatment of systematic and random errors in the constraining data, and in the model being constrained, are crucial if this methodology is to be used to test hypotheses relating to the physics of galaxy formation.

### Cookie-cutter halos: the remarkable constancy of the stellar mass function of satellite galaxies at 0.2<z<1.2

We present an observational study of the stellar mass function of satellite galaxies around central galaxies at 0.2<z<1.2. Using statistical background subtraction of contaminating sources we derive satellite stellar mass distributions in four bins of central galaxy mass in three redshift ranges. Our results show that the stellar mass function of satellite galaxies increases with central galaxy mass, and that the distribution of satellite masses at fixed central mass is at most weakly dependent on redshift. We conclude that the average mass distribution of galaxies in groups is remarkably universal even out to z=1.2 and that it can be uniquely characterized by the group central galaxy mass. This further suggests that as central galaxies grow in stellar mass, they do so in tandem with the mass growth of their satellites. Finally, we classify all galaxies as either star forming or quiescent, and derive the mass functions of each subpopulation separately. We find that the mass distribution of both star forming and quiescent satellites show minimal redshift dependence at fixed central mass. However, while the fraction of quiescent satellite galaxies increases rapidly with increasing central galaxy mass, that of star forming satellites decreases.

### Inference of the Cold Dark Matter substructure mass function at z=0.2 using strong gravitational lenses

We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68 percent confidence level and a substructure mass function slope $\alpha$ < 2.93 at the 95 percent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ = 1.90$^{+0.98}_{-1.98}$ at the 68 percent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models).The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 percent confidence level.

### Inference of the Cold Dark Matter substructure mass function at z=0.2 using strong gravitational lenses [Replacement]

We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc squared around the Einstein radius (~4.2 kpc). We infer a mean projected substructure mass fraction $f = 0.0076^{+0.0208}_{-0.0052}$ at the 68 percent confidence level and a substructure mass function slope $\alpha$ < 2.93 at the 95 percent confidence level for a uniform prior probability density on alpha. For a Gaussian prior based on Cold Dark Matter (CDM) simulations, we infer $f = 0 .0064^{+0.0080}_{-0.0042}$ and a slope of $\alpha$ = 1.90$^{+0.098}_{-0.098}$ at the 68 percent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models).The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 percent confidence level.

### The Effect of Orbital Eccentricity on the Dynamical Evolution of Star Clusters

We use N-body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters on circular and eccentric orbits. For a given perigalactic distance, increasing orbital eccentricity slows the dynamical evolution of a cluster due to a weaker mean tidal field. However, we find that perigalactic passes and tidal heating due to an eccentric orbit can partially compensate for the decreased mean tidal field by energizing stars to higher velocities and stripping additional stars from the cluster, accelerating the relaxation process. We find that the corresponding circular orbit which best describes the evolution of a cluster on an eccentric orbit is much less than its semi-major axis or time averaged galactocentric distance. Since clusters spend the majority of their lifetimes near apogalacticon, the properties of clusters which appear very dynamically evolved for a given galactocentric distance can be explained by an eccentric orbit. Additionally we find that the evolution of the slope of the mass function within the core radius is roughly orbit-independent, so it could place additional constraints on the initial mass and initial size of globular clusters with solved orbits. We use our results to demonstrate how the orbit of Milky Way globular clusters can be constrained given standard observable parameters like galactocentric distance and the slope of the mass function. We then place constraints on the unsolved orbits of NGC 1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass functions.

### The Effect of Orbital Eccentricity on the Dynamical Evolution of Star Clusters [Replacement]

We use N-body simulations to explore the influence of orbital eccentricity on the dynamical evolution of star clusters. Specifically we compare the mass loss rate, velocity dispersion, relaxation time, and the mass function of star clusters on circular and eccentric orbits. For a given perigalactic distance, increasing orbital eccentricity slows the dynamical evolution of a cluster due to a weaker mean tidal field. However, we find that perigalactic passes and tidal heating due to an eccentric orbit can partially compensate for the decreased mean tidal field by energizing stars to higher velocities and stripping additional stars from the cluster, accelerating the relaxation process. We find that the corresponding circular orbit which best describes the evolution of a cluster on an eccentric orbit is much less than its semi-major axis or time averaged galactocentric distance. Since clusters spend the majority of their lifetimes near apogalacticon, the properties of clusters which appear very dynamically evolved for a given galactocentric distance can be explained by an eccentric orbit. Additionally we find that the evolution of the slope of the mass function within the core radius is roughly orbit-independent, so it could place additional constraints on the initial mass and initial size of globular clusters with solved orbits. We use our results to demonstrate how the orbit of Milky Way globular clusters can be constrained given standard observable parameters like galactocentric distance and the slope of the mass function. We then place constraints on the unsolved orbits of NGC 1261,NGC 6352, NGC 6496, and NGC 6304 based on their positions and mass functions.

### Radial variations in the stellar initial mass function of early-type galaxies

The hypothesis of a universal initial mass function (IMF) — motivated by observations in nearby stellar systems — has been recently challenged by the discovery of an IMF systematic variation with the central velocity dispersion, {\sigma}, of early-type galaxies (ETGs), towards an excess of low-mass stars in high {\sigma} galaxies. This trend has been found to hold for the central regions of ETGs, and remains unexplained at the present. To shed new lights on it, we have obtained new, extremely deep, spectroscopy, for three nearby ETGs, two with high {\sigma} (~300 km/s), and one low-mass system, with {\sigma} ~ 100 km/s. From the analysis of IMF-sensitive spectral features, we find that the IMF depends significantly on galactocentric distance in the massive ETGs, with the enhanced fraction of low-mass stars confined to their central regions. For the low-{\sigma} galaxy, no significant radial gradient is detected in the IMF, which is well described by a Milky-Way-like distribution at all radii. Such a result suggests that the IMF should be regarded as a local (rather than global) galaxy property, and suggests a significant difference in the formation process of the core and the outskirts of massive galaxies.

### What do simulations predict for the galaxy stellar mass function and its evolution in different environments?

We present a comparison between the observed galaxy stellar mass function and the one predicted from the De Lucia & Blaizot (2007) semi-analytic model applied to the Millennium Simulation, for cluster satellites and galaxies in the field (meant as a wide portion of the sky, including all environments), in the local universe (z~0.06) and at intermediate redshift (z~0.6), with the aim to shed light on the processes which regulate the mass distribution in different environments. While the mass functions in the field and in its finer environments (groups, binary and single systems) are well matched in the local universe down to the completeness limit of the observational sample, the model over-predicts the number of low mass galaxies in the field at z~0.6 and in clusters at both redshifts. Above M_*=10^10.25 M_sun, it reproduces the observed similarity of the cluster and field mass functions, but not the observed evolution. Our results point out two shortcomings of the model: an incorrect treatment of cluster-specific environmental effects and an over-efficient galaxy formation at early times (as already found by e.g. Weinmann et al. 2012). Next, we consider only simulations. Using also the Guo et al. (2011) model, we find that the high mass end of the mass functions depends on halo mass: only very massive halos host massive galaxies, with the result that their mass function is flatter. Above M_*=10^9.4 M_sun, simulations show an evolution in the number of the most massive galaxies in all the environments. Mass functions obtained from the two prescriptions are different, however results are qualitatively similar, indicating that the adopted recipes to model the evolution of central and satellite galaxies still have to be better implemented in semi-analytic models.

### Direct $N$-body simulations of globular clusters - II. Palomar 4

We use direct $N$-body calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime in order to reproduce its observed mass, half-light radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a non-mass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4′s overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reproduce the observed amount of mass segregation and mass function flattening simultaneously. Unresolved binaries cannot reconcile this discrepancy either. We find that only models with both a flattened IMF and primordial segregation are able to fit the observations. The initial (i.e. after gas expulsion) mass and half-mass radius of Pal~4 in this case are about 57000 M${\odot}$ and 10 pc, respectively. This configuration is more extended than most globular clusters we observe, showing that the conditions under which Pal~4 formed must have been significantly different from that of the majority of globular clusters. We discuss possible scenarios for such an unusual configuration of Pal~4 in its early years.

### Variations in the initial mass function in early-type galaxies: A critical comparison between dynamical and spectroscopic results

I present a comparison between published dynamical (ATLAS3D) and spectroscopic (Conroy & van Dokkum) constraints on the stellar initial mass function (IMF) in early-type galaxies, using the 34 galaxies in common between the two works. Both studies infer an average IMF mass factor $\alpha$ (the stellar mass relative to a Kroupa-IMF population of similar age and metallicity) greater than unity, i.e. both methods favour an IMF which is heavier than that of the Milky Way, on average over the sample. However, on a galaxy-by-galaxy basis, there is no correlation between $\alpha$ inferred from the two approaches. I investigate how the two estimates of $\alpha$ are correlated systematically with the galaxy velocity dispersion, $\sigma$, and with the Mg/Fe abundance ratio. The spectroscopic method, based on the strengths of metal absorption lines, yields a correlation only with metal abundance ratios: at fixed Mg/Fe, there is no residual correlation with $\sigma$. The dynamical method, applied to exactly the same galaxy sample, yields the opposite result: the IMF variation correlates only with dynamics, with no residual correlation with Mg/Fe after controlling for $\sigma$. Hence although both methods indicate a heavy IMF on average in ellipticals, they lead to incompatible results for the systematic trends, when applied to the same set of galaxies. Although other explanations are possible, the sense of the disagreement suggests that one (or both) of the methods has not accounted fully for the main confounding factors, i.e. element abundance ratios or dark matter contributions.

### Variations in the initial mass function in early-type galaxies: A critical comparison between dynamical and spectroscopic results [Replacement]

I present a comparison between published dynamical (ATLAS3D) and spectroscopic (Conroy & van Dokkum) constraints on the stellar initial mass function (IMF) in early-type galaxies, using the 34 galaxies in common between the two works. Both studies infer an average IMF mass factor $\alpha$ (the stellar mass relative to a Kroupa-IMF population of similar age and metallicity) greater than unity, i.e. both methods favour an IMF which is heavier than that of the Milky Way, on average over the sample. However, on a galaxy-by-galaxy basis, there is no correlation between $\alpha$ inferred from the two approaches. I investigate how the two estimates of $\alpha$ are correlated systematically with the galaxy velocity dispersion, $\sigma$, and with the Mg/Fe abundance ratio. The spectroscopic method, based on the strengths of metal absorption lines, yields a correlation only with metal abundance ratios: at fixed Mg/Fe, there is no residual correlation with $\sigma$. The dynamical method, applied to exactly the same galaxy sample, yields the opposite result: the IMF variation correlates only with dynamics, with no residual correlation with Mg/Fe after controlling for $\sigma$. Hence although both methods indicate a heavy IMF on average in ellipticals, they lead to incompatible results for the systematic trends, when applied to the same set of galaxies. The sense of the disagreement could suggest that one (or both) of the methods has not accounted fully for the main confounding factors, i.e. element abundance ratios or dark matter contributions. Alternatively, the poor agreement might indicate additional variation in the detailed shape of the IMF, beyond what can currently be inferred from the spectroscopic features.

### Gaia photometry for white dwarfs

Context. White dwarfs can be used to study the structure and evolution of the Galaxy by analysing their luminosity function and initial mass function. Among them, the very cool white dwarfs provide the information for the early ages of each population. Because white dwarfs are intrinsically faint only the nearby (about 20 pc) sample is reasonably complete. The Gaia space mission will drastically increase the sample of known white dwarfs through its 5-6 years survey of the whole sky up to magnitude V = 20-25. Aims. We provide a characterisation of Gaia photometry for white dwarfs to better prepare for the analysis of the scientific output of the mission. Transformations between some of the most common photometric systems and Gaia passbands are derived. We also give estimates of the number of white dwarfs of the different galactic populations that will be observed. Methods. Using synthetic spectral energy distributions and the most recent Gaia transmission curves, we computed colours of three different types of white dwarfs (pure hydrogen, pure helium, and mixed composition with H/He= 0.1). With these colours we derived transformations to other common photometric systems (Johnson-Cousins, Sloan Digital Sky Survey, and 2MASS). We also present numbers of white dwarfs predicted to be observed by Gaia. Results. We provide relationships and colour-colour diagrams among different photometric systems to allow the prediction and/or study of the Gaia white dwarf colours. We also include estimates of the number of sources expected in every galactic population and with a maximum parallax error. Gaia will increase the sample of known white dwarfs tenfold to about 200 000. Gaia will be able to observe thousands of very cool white dwarfs for the first time, which will greatly improve our understanding of these stars and early phases of star formation in our Galaxy.

### Cosmology with Galaxy Clusters: Systematic Effects in the Halo Mass Function [Replacement]

We investigate potential systematic effects in constraining the amplitude of primordial fluctuations \sigma_8 arising from the choice of halo mass function in the likelihood analysis of current and upcoming galaxy cluster surveys. We study the widely used N-body simulation fit of Tinker et al. (T08) and, as an alternative, the recently proposed analytical model of Excursion Set Peaks (ESP). We first assess the relative bias between these prescriptions when constraining \sigma_8 by sampling the ESP mass function to generate mock catalogs and using the T08 fit to analyse them, for various choices of survey selection threshold, mass definition and statistical priors. To assess the level of absolute bias in each prescription, we then repeat the analysis on dark matter halo catalogs in N-body simulations designed to mimic the mass distribution in the current data release of Planck SZ clusters. This N-body analysis shows that using the T08 fit without accounting for the scatter introduced when converting between mass definitions (alternatively, the scatter induced by errors on the parameters of the fit) can systematically over-estimate the value of \sigma_8 by as much as 2\sigma\ for current data, while analyses that account for this scatter should be close to unbiased in \sigma_8. With an increased number of objects as expected in upcoming data releases, regardless of accounting for scatter, the T08 fit could over-estimate the value of \sigma_8 by ~1.5\sigma. The ESP mass function leads to systematically more biased but comparable results. A strength of the ESP model is its natural prediction of a weak non-universality in the mass function which closely tracks the one measured in simulations and described by the T08 fit. We suggest that it might now be prudent to build new unbiased ESP-based fitting functions for use with the larger datasets of the near future.

### Cosmology with Galaxy Clusters: Systematic Effects in the Halo Mass Function

We investigate potential systematic effects in constraining the amplitude of primordial fluctuations \sigma_8 arising from the choice of halo mass function in the likelihood analysis of current and upcoming galaxy cluster surveys. We study the widely used N-body simulation fit of Tinker et al. (T08) and, as an alternative, the recently proposed analytical model of Excursion Set Peaks (ESP). We first assess the relative bias between these prescriptions when constraining \sigma_8 by sampling the ESP mass function to generate mock catalogs and using the T08 fit to analyse them, for various choices of survey selection threshold, mass definition and statistical priors. To assess the level of absolute bias in each prescription, we then repeat the analysis on dark matter halo catalogs in N-body simulations designed to mimic the mass distribution in the current data release of Planck SZ clusters. This N-body analysis shows that using the T08 fit without accounting for the scatter introduced when converting between mass definitions (alternatively, the scatter induced by errors on the parameters of the fit) can systematically over-estimate the value of \sigma_8 by as much as 2\sigma\ for current data, while analyses that account for this scatter should be close to unbiased in \sigma_8. With an increased number of objects as expected in upcoming data releases, regardless of accounting for scatter, the T08 fit could over-estimate the value of \sigma_8 by ~1.5\sigma. The ESP mass function leads to systematically more biased but comparable results. A strength of the ESP model is its natural prediction of a weak non-universality in the mass function which closely tracks the one measured in simulations and described by the T08 fit. We suggest that it might now be prudent to build new unbiased ESP-based fitting functions for use with the larger datasets of the near future.

### Setting new Cosmology constraints with ALMA

I make a short revision of Cosmology questions which ALMA was built to address. Without diving into much detail, I point out the ALMA specifications and strategies which are expected to provide a better handle of: the temperature evolution of the Cosmic Microwave Background (CMB) and the properties of its secondary anisotropies (such as the thermal and kinetic Sunyaev-Zel’dovich and the Ostriker-Vishniac effects); variability of dimensionless fundamental constants; Ho and galaxy initial mass function by means of strong gravitational lensing; black hole science with the greatly expected Event Horizon Telescope.

### Setting new Cosmology constraints with ALMA [Replacement]

I make a short revision of Cosmology questions which ALMA was built to address. Without diving into much detail, I point out the ALMA specifications and strategies which are expected to provide a better handle of: the temperature evolution of the Cosmic Microwave Background (CMB) and the properties of its secondary anisotropies (such as the thermal and kinetic Sunyaev-Zel’dovich and the Ostriker-Vishniac effects); variability of dimensionless fundamental constants; Ho and galaxy initial mass function by means of strong gravitational lensing; black hole science with the greatly expected Event Horizon Telescope.

### A Model for Multi-property Galaxy Cluster Statistics

The massive dark matter halos that host groups and clusters of galaxies have observable properties that appear to be log-normally distributed about power-law mean scaling relations in halo mass. Coupling this assumption with either quadratic or cubic approximations to the mass function in log space, we derive closed-form expressions for the space density of halos as a function of multiple observables as well as forms for the low-order moments of properties of observable-selected samples. Using a Tinker mass function in a {\Lambda}CDM cosmology, we show that the cubic analytic model reproduces results obtained from direct, numerical convolution at the 10 percent level or better over nearly the full range of observables covered by current observations and for redshifts extending to z = 1.5. The model provides an efficient framework for estimating effects arising from selection and covariance among observable properties in survey samples.

### 350 $\mu$m map of the Ophiuchus molecular cloud: core mass function [Replacement]

Stars are born in dense cores of molecular clouds. The core mass function (CMF), which is the mass distribution of dense cores, is important for understanding the stellar initial mass function (IMF). We obtained 350 $\mu$m dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory (CSO) telescope. A 350 $\mu$m map covering 0.25 ${deg}^{2}$ of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9 $^{\prime\prime}$, corresponding to $1.2\times {10}^{3}\$AU at the distance of the Ophiuchus molecular cloud (131 pc). The data was reduced using the Comprehensive Reduction Utility for SHARC-II (CRUSH). The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores (a subcategory of starless cores) were also identified. The excitation temperatures, which were derived from FCRAO ${}^{12}$CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with $\mu =-1.18\pm0.10,\ \sigma =0.58\pm0.05$ and $\mu =1.40\pm0.10,\ \sigma =0.50\pm0.05$ respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.

### 350 $\mu$m map of the Ophiuchus molecular cloud: core mass function [Replacement]

Stars are born in dense cores of molecular clouds. The core mass function (CMF), which is the mass distribution of dense cores, is important for understanding the stellar initial mass function (IMF). We obtained 350 $\mu$m dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory (CSO) telescope. A 350 $\mu$m map covering 0.25 ${deg}^{2}$ of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9 $^{\prime\prime}$, corresponding to $1.2\times {10}^{3}\$AU at the distance of the Ophiuchus molecular cloud (131 pc). The data was reduced using the Comprehensive Reduction Utility for SHARC-II (CRUSH). The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores (a subcategory of starless cores) were also identified. The excitation temperatures, which were derived from FCRAO ${}^{12}$CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with $\mu =-1.18\pm0.10,\ \sigma =0.58\pm0.05$ and $\mu =1.40\pm0.10,\ \sigma =0.50\pm0.05$ respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.

### 350 $\mu$m map of the Ophiuchus molecular cloud: core mass function [Replacement]

Stars are born in dense cores of molecular clouds. The core mass function (CMF), which is the mass distribution of dense cores, is important for understanding the stellar initial mass function (IMF). We obtained 350 $\mu$m dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory (CSO) telescope. A 350 $\mu$m map covering 0.25 ${deg}^{2}$ of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9 $^{\prime\prime}$, corresponding to $1.2\times {10}^{3}\$AU at the distance of the Ophiuchus molecular cloud (131 pc). The data was reduced using the Comprehensive Reduction Utility for SHARC-II (CRUSH). The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores (a subcategory of starless cores) were also identified. The excitation temperatures, which were derived from FCRAO ${}^{12}$CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with $\mu =-1.18\pm0.10,\ \sigma =0.58\pm0.05$ and $\mu =1.40\pm0.10,\ \sigma =0.50\pm0.05$ respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.

### 350 $\mu$m map of the Ophiuchus molecular cloud: core mass function

Stars are born in dense cores of molecular clouds. The core mass function (CMF), which is the mass distribution of dense cores, is important for understanding the stellar initial mass function (IMF). We obtained 350 $\mu$m dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory (CSO) telescope. A 350 $\mu$m map covering 0.25 ${deg}^{2}$ of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9 $^{\prime\prime}$, corresponding to $1.2\times {10}^{3}\$AU at the distance of the Ophiuchus molecular cloud (131 pc). The data was reduced using the Comprehensive Reduction Utility for SHARC-II (CRUSH). The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores (a subcategory of starless cores) were also identified. The excitation temperatures, which were derived from FCRAO ${}^{12}$CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with $\mu =-1.18\pm0.10,\ \sigma =0.58\pm0.05$ and $\mu =1.40\pm0.10,\ \sigma =0.50\pm0.05$ respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.

### Salpeter normalization of the Stellar Initial Mass Function for massive galaxies at z~1

The stellar initial mass function (IMF) is a key parameter to study galaxy evolution. Here we measure the IMF mass normalization for a sample of 68 field galaxies in the redshift range 0.7 to 0.9 within the Extended Groth Strip. To do this we derive total (stellar + dark matter) mass-to-light [$(M/L)_{\rm dyn}$] using axisymmetric dynamical models. Within the region where we have kinematics (about one half-light radius), the models assume: (i) that mass-follows-light, implying negligible differences between the stellar and total density profiles; (ii) constant velocity anisotropy ($\beta_{\rm z}\equiv1-\sigma_z^2/\sigma_R^2=0.2$); (iii) that galaxies are seen at the average inclination for random orientations (i.e. $i=60^\circ$, where $i=90^\circ$ represents edge-on). The dynamical models are based on anisotropic Jeans equations, constrained by HST/ACS imaging and the central velocity dispersion of the galaxies, extracted from good-quality spectra taken by the DEEP2 survey. The population $(M/L)_{\rm pop}$ are derived from full-spectrum fitting of the same spectra with a grid of simple stellar population models. Recent dynamical modelling results by the $ATLAS^{3D}$ project and numerical simulations of galaxy evolution indicate that the dark matter fraction within the central regions of our galaxies should be small. This suggest that our derived total $(M/L)_{\rm dyn}$ should closely approximate the stellar $M/L$. Our comparison of $(M/L)_{\rm dyn}$ and $(M/L)_{\rm pop}$ then imply that for galaxies with stellar mass $M_\odot \geq 10^{11}$ $M_{\odot}$, the $average$ normalization of the IMF is consistent with a Salpeter slope, with a substantial scatter. This is similar to what is found within a similar mass range for nearby galaxies.