We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, ...hence the lens cross section, for realistic lens profiles. We find that, for essentially the full range of parameters either observationally determined or yielded by numerical simulations, the combination of dark matter and star distribution can be very well described, for lens radii relevant to strong lensing, by a simple power law whose slope is very weakly dependent on the parameters characterizing the global matter surface density profile and close to isothermal in agreement with direct estimates for individual lens galaxies. Our simple treatment allows an easy insight into the role of the different ingredients that determine the lens cross section and the distribution of gravitational amplifications. They also ease the reconstruction of the lens mass distribution from the observed images and, vice versa, allow a fast application of ray-tracing techniques to model the effect of lensing on a variety of source structures. The maximum amplification depends primarily on the source size. Amplifications larger than approx =20 are indicative of compact source sizes at high-z, in agreement with expectations if galaxies formed most of their stars during the dissipative collapse of cold gas. Our formalism has allowed us to reproduce the counts of strongly lensed galaxies found in the H-ATLAS Science Demonstration Phase field. While our analysis is focused on spherical lenses, we also discuss the effect of ellipticity and the case of late-type lenses (showing why they are much less common, even though late-type galaxies are more numerous). Furthermore, we discuss the effect of a cluster halo surrounding the early-type lens and of a supermassive black hole at its center.
ABSTRACT
We have performed a detailed analysis of the local supermassive black hole (SMBH) mass function based on both kinematic and photometric data and we have derived an accurate analytical fit in ...the range 106≤MBH/M⊙≤ 5 × 109. We find a total SMBH mass density of (4.2 ± 1.1) × 105 M⊙ Mpc−3, about 25 per cent of which is contributed by SMBHs residing in bulges of late‐type galaxies. Exploiting up‐to‐date luminosity functions of hard X‐ray and optically selected active galactic nuclei (AGNs), we have studied the accretion history of the SMBH population. If most of the accretion occurs at constant , as in the case of Eddington‐limited accretion and consistent with recent observational estimates, the local SMBH mass function is fully accounted for by mass accreted by X‐ray selected AGNs, with bolometric corrections indicated by current observations and a standard mass‐to‐light conversion efficiency ε≃ 10 per cent. The analysis of the accretion history highlights that the most massive BHs (associated with bright optical quasi‐stellar objects) accreted their mass faster and at higher redshifts (typically at z > 1.5), while the lower‐mass BHs responsible for most of the hard X‐ray background have mostly grown at z < 1.5. The accreted mass function matches the local SMBH mass function if, during the main accretion phases, ε≃ 0.09 (+0.04, −0.03) and the Eddington ratio λ=L/LEdd≃ 0.3 (+0.3, −0.1) (68 per cent confidence errors). The visibility time, during which AGNs are luminous enough to be detected by the currently available X‐ray surveys, ranges from ≃0.1 Gyr for present‐day BH masses M0BH≃ 106 M⊙ to ≃0.3 Gyr for M0BH≥ 109 M⊙. The mass accreted during luminous phases is ≥25–30 per cent even if we assume extreme values of ε(ε≃ 0.3–0.4). An unlikely fine tuning of the parameters would be required to account for the local SMBH mass function accommodating a dominant contribution from ‘dark’ BH growth (due, for example, to BH coalescence).
Exploiting the Herschel Astrophysical Terahertz Large Area Survey Science Demonstration Phase survey data, we have determined the luminosity functions (LFs) at rest-frame wavelengths of 100 and 250 ...Delta *mm and at several redshifts z 1, for bright submillimeter galaxies with star formation rates (SFRs) 100 M yr--1. We find that the evolution of the comoving LF is strong up to z 2.5, and slows down at higher redshifts. From the LFs and the information on halo masses inferred from clustering analysis, we derived an average relation between SFR and halo mass (and its scatter). We also infer that the timescale of the main episode of dust-enshrouded star formation in massive halos (M H 3 X 1012 M ) amounts to ~7 X 108 yr. Given the SFRs, which are in the range of 102-103 M yr--1, this timescale implies final stellar masses of the order of 1011-1012 M . The corresponding stellar mass function matches the observed mass function of passively evolving galaxies at z 1. The comparison of the statistics for submillimeter and UV-selected galaxies suggests that the dust-free, UV bright phase is 102 times shorter than the submillimeter bright phase, implying that the dust must form soon after the onset of star formation. Using a single reference spectral energy distribution (SED; the one of the z 2.3 galaxy SMM J2135-0102), our simple physical model is able to reproduce not only the LFs at different redshifts >1 but also the counts at wavelengths ranging from 250 Delta *mm to 1 mm. Owing to the steepness of the counts and their relatively broad frequency range, this result suggests that the dispersion of submillimeter SEDs of z > 1 galaxies around the reference one is rather small.
We report on deep near-infrared observations obtained with the Wide Field Camera-3 (WFC3) onboard the Hubble Space Telescope (HST) of the first five confirmed gravitational lensing events discovered ...by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). We succeed in disentangling the background galaxy from the lens to gain separate photometry of the two components. The HST data allow us to significantly improve on previous constraints of the mass in stars of the lensed galaxy and to perform accurate lens modelling of these systems, as described in the accompanying paper by Dye et al. We fit the spectral energy distributions of the background sources from near-IR to millimetre wavelengths and use the magnification factors estimated by Dye et al. to derive the intrinsic properties of the lensed galaxies. We find these galaxies to have star-formations rates (SFR) ~ 400-2000 M... yr..., with ~(6-25) x ... of their baryonic mass already turned into stars. At these rates of star formation, all remaining molecular gas will be exhausted in less than ~100 Myr, reaching a final mass in stars of a few ... These galaxies are thus proto-ellipticals caught during their major episode of star formation, and observed at the peak epoch (z ~ 1.5-3) of the cosmic star formation history of the Universe. (ProQuest: ... denotes formulae/symbols omitted.)
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.
Aims. The paper is devoted to the study of the underlying stellar population of a sample of 65 nearby early-type galaxies, predominantly located in low density environments, a large fraction of which ...show emission lines. Methods. Ages, metallicities, and \alpha/Fe ratios have been derived through the comparison of Lick indices measured at different galacto- centric distances (7 apertures and 4 gradients) with new simple stellar population (SSP) models that account for the presence of \alpha/Fe- enhancement. The SSPs cover a wide range of ages ( 10 super(9)-16 \times 10 super(9) yr), metallicities (0.0004 \le Z \le0.05), and \alpha/Fe ratios (0-0.8). To derive the stellar population parameters, we use an algorithm that provides, together with the most likely solution in the (age, Z, \alpha/Fe) space, the probability density function along the age-metallicity degeneracy. Results. We derive a large spread in age, with SSP-equivalent ages ranging from a few to 15 Gyr. Age does not show any significant trend with central velocity dispersion \sigma_{\rm c}, but E galaxies appear on average older than lenticulars. On the contrary, a significant increasing trend of metallicity and \alpha/Fe with \sigma_{\rm c} is observed, testifying that the chemical enrichment was more efficient and the duration of the star formation shorter in more massive galaxies. These latter two relations do not depend on galaxy morphological type. We have also sought possible correlations with the local galaxy density \rho_{xyz}, but neither metallicity nor \alpha-enhancement show clear trends. However, we find that while low density environments (LDE) ( \rho_{xyz} \le 0.4) contain very young objects (from 1 Gyr to 4 Gyr), none of the galaxies in the higher density environments (HDE) (40% of galaxies with a measured density) is younger than 5 Gyr. Considering the lack of environmental effect on the \alpha/Fe ratio and the high value of \alpha/Fe in some young massive objects, we argue that young galaxies in LDE are more likely due to recent rejuvenation episodes. By comparing the number of "rejuvenated" objects with the total number of galaxies in our sample, and by means of simple two-SSP component models, we estimate that, on average, the rejuvenation episodes do not involve more than 25% of the total galaxy mass. The good quality of the data also allow us to analyze the gradients of stellar populations. An average negative metallicity gradient \Delta \log Z/\Delta \log (r/r_{\rm e}) \sim- 0.21 is firmly detected, while the age and \alpha-enhancement spatial distributions within r_{\rm e}/2 appear quite flat. These observations suggest that, in a given galaxy, the star formation proceeded on similar timescales all across the central r_{\rm e}/2 region, but with an increasing efficiency toward the center.
An unambiguous manifestation of the magnification bias is the cross-correlation between two source samples with non-overlapping redshift distributions. In this work we measure and study the ...cross-correlation signal between a foreground sample of GAMA galaxies with spectroscopic redshifts in the range 0.2< z <0.8, and a background sample of H-ATLAS galaxies with photometric redshifts ∼>1.2. It constitutes a substantial improvement over the cross-correlation measurements made by Gonzalez-Nuevo et al. (2014) with updated catalogues and wider area (with S / N ∼> 5 below 10 arcmin and reaching S / N ∼ 20 below 30 arcsec). The better statistics allow us to split the sample in different redshift bins and to perform a tomographic analysis (with S / N ∼> 3 below 10 arcmin and reaching S / N ∼ 15 below 30 arcsec). Moreover, we implement a halo model to extract astrophysical information about the background galaxies and the deflectors that are producing the lensing link between the foreground (lenses) and background (sources) samples. In the case of the sources, we find typical mass values in agreement with previous studies: a minimum halo mass to host a central galaxy, M {sub min}∼ 10{sup 12.26} M {sub ⊙}, and a pivot halo mass to have at least one sub-halo satellite, M {sub 1∼} 10{sup 12.84} M {sub ⊙}. However, the lenses are massive galaxies or even galaxy groups/clusters, with minimum mass of M {sub min}{sup lens}∼ 10{sup 13.06} M {sub ⊙}. Above a mass of M {sub 1}{sup lens}∼ 10{sup 14.57} M {sub ⊙} they contain at least one additional satellite galaxy which contributes to the lensing effect. The tomographic analysis shows that, while M {sub 1}{sup lens} is almost redshift independent, there is a clear evolution of increase M {sub min}{sup lens} with redshift in agreement with theoretical estimations. Finally, the halo modeling allows us to identify a strong lensing contribution to the cross-correlation for angular scales below 30 arcsec. This interpretation is supported by the results of basic but effective simulations.
While continuum imaging data at far-infrared to submillimetre wavelengths have provided tight constraints on the population properties of dusty star-forming galaxies up to high redshifts, future ...space missions like the Space Infrared Telescope for Cosmology and Astrophysics (SPICA) and ground-based facilities like the Cerro Chajnantor Atacama Telescope (CCAT) will allow detailed investigations of their physical properties via their mid-/far-infrared line emission. We present updated predictions for the number counts and the redshift distributions of star-forming galaxies spectroscopically detectable by these future missions. These predictions exploit a recent upgrade of evolutionary models, that include the effect of strong gravitational lensing, in the light of the most recent Herschel and South Pole Telescope data. Moreover the relations between line and continuum infrared luminosity are re-assessed, considering also differences among source populations, with the support of extensive simulations that take into account dust obscuration. The derived line luminosity functions are found to be highly sensitive to the spread of the line to continuum luminosity ratios. Estimates of the expected numbers of detections per spectral line by SPICA/SpicA FAR-infrared Instrument (SAFARI) and by CCAT surveys for different integration times per field of view at fixed total observing time are presented. Comparing with the earlier estimates by Spinoglio et al. we find, in the case of SPICA/SAFARI, differences within a factor of 2 in most cases, but occasionally much larger. More substantial differences are found for CCAT.
Direct and indirect observational evidence leads to the conclusion that high-redshift QSOs did shine in the core of early-type protogalaxies during their main episode of star formation. Exploiting ...this fact, we derive the rate of formation of this kind of stellar system at high redshift by using the QSO luminosity function. The elemental proportions in elliptical galaxies, the descendants of the QSO hosts, suggest that the star formation was more rapid in more massive objects. We show that this is expected to occur in dark matter haloes, when the processes of cooling and heating are considered. This is also confirmed by comparing the observed submm counts with those derived by coupling the formation rate and the star formation rate of the spheroidal galaxies with a detailed model for their SED evolution. In this scenario SCUBA galaxies and Lyman-break galaxies are early-type protogalaxies forming the bulk of their stars before the onset of QSO activity.
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