arXiv subjects

Simone Bianchi

Publications and source records attributed to Simone Bianchi.

At least 55 records · Page 3Linked to original sources

arXiv2016

The Herschel Virgo Cluster Survey. XIX. Physical properties of low luminosity FIR sources at $z <$ 0.5

The Star formation rate (SFR) is a crucial parameter to investigate galaxy evolution. At low redshift the cosmic SFR density declines smoothly, and massive active galaxies become passive, reducing their star formation activity. This implies that the bulk of the SFR density at low redshift is mainly driven by low mass objects. We investigate the properties of a sample of low luminosity Far-Infrared (FIR) sources selected at 250 microns from Pappalardo et al. (2015). We have collected data from Ultraviolet to FIR to perform a multi-wavelengths analysis. The main goal is to investigate the correlation between SFR, stellar mass, and dust mass for a galaxy population with a wide range in dust content and stellar mass, including the low mass regime that most probably dominates the SFR density at low z. We define a main sample of ~800 sources with full Spectral Energy Distribution (SED) coverage between 0.15 < lambda < 500 microns and an extended sample with ~5000 sources in which we remove the constraints on the Ultraviolet and Near-Infrared bands. We analyze both samples with two different SED fitting methods: MAGPHYS and CIGALE. In the SFR versus stellar mass plane our samples occupy a region included between local spirals and higher redshift star forming galaxies. The galaxies subsample with the higher masses (M* > 3e10 Msol) does not lie on the main sequence, but shows a small offset, as a consequence of the decreased star formation. Low mass galaxies (M* < 1e10 Msol) settle in the main sequence with SFR and stellar mass consistent with local spirals. Deep Herschel data allow the identification of a mixed galaxy population, with galaxies still in an assembly phase, or galaxies at the beginning of their passive evolution. We find that the dust luminosity is the parameter that discriminates these two galaxy populations.

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arXiv2016

Composite biasing in Monte Carlo radiative transfer

Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the specific problems that we consider: in simulations with composite path length stretching, high accuracy results are obtained even for simulations with modest numbers of photon packages, while simulations without biasing cannot reach convergence, even with a huge number of photon packages.

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arXiv2015

Benchmarking the Calculation of Stochastic Heating and Emissivity of Dust Grains in the Context of Radiative Transfer Simulations

We define an appropriate problem for benchmarking dust emissivity calculations in the context of radiative transfer (RT) simulations, specifically including the emission from stochastically heated dust grains. Our aim is to provide a self-contained guide for implementors of such functionality, and to offer insights in the effects of the various approximations and heuristics implemented by the participating codes to accelerate the calculations. The benchmark problem definition includes the optical and calorimetric material properties, and the grain size distributions, for a typical astronomical dust mixture with silicate, graphite and PAH components; a series of analytically defined radiation fields to which the dust population is to be exposed; and instructions for the desired output. We process this problem using six RT codes participating in this benchmark effort, and compare the results to a reference solution computed with the publicly available dust emission code DustEM. The participating codes implement different heuristics to keep the calculation time at an acceptable level. We study the effects of these mechanisms on the calculated solutions, and report on the level of (dis)agreement between the participating codes. For all but the most extreme input fields, we find agreement within 10% across the important wavelength range from 3 to 1000 micron. We conclude that the relevant modules in RT codes can and do produce fairly consistent results for the emissivity spectra of stochastically heated dust grains.

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arXiv2015

The origin of the Far-infrared continuum of z ~ 6 quasars: a radiative transfer model for SDSS J1148+5251

We investigate the origin of the FIR continuum of SDSS J1148+5251, using it as a prototype for the more general class of high-luminosity high-redshift QSOs. We run the radiative transfer code TRADING to follow the transfer of radiation from the central source and from stellar sources through the dusty environment of the host galaxy. The model is based on the output of the semi-analytical merger tree code, GAMETE/QSOdust, which enables to predict the evolution of the host galaxy and of its nuclear black hole, following the star formation history and chemical evolution -- including dust -- in all the progenitor galaxies of SDSS J1148+5251. We find that the radiation emitted by the central source can also provide an important source of heating for the dust distributed in the host galaxy, powering at least 30% and up to 70% of the observed far infrared emission at rest-frame wavelengths [20 - 1000]micron. The remaining fraction is contributed by stellar sources and can only be achieved if the host galaxy is able to sustain a star formation rate of ~ 900 Msun/yr at z=6.4. This points to a co-evolution scenario where, during their hierarchical assembly, the first SMBHs and their host galaxies first grow at the same pace until the black hole reaches a mass of ~ 2 10^8 Msun and starts growing faster than its host, reaching the bright quasar phase when the black hole and stellar mass fall within the scatter of the scaling relation observed in local galaxies. This same evolutionary scenario has been recently shown to explain the properties of a larger sample of 5 < z <6.4 QSOs, and imply that current dynamical mass measurements may have missed an important fraction of the host galaxy stellar mass. We conclude that the FIR luminosity of high-z quasars is a sensitive tracer of the rapidly changing physical conditions in the host galaxy.

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arXiv2014

The Herschel Virgo Cluster Survey. XVII. SPIRE point-source catalogs and number counts

We present three independent catalogs of point-sources extracted from SPIRE images at 250, 350, and 500 micron as a part of the Herschel Virgo Cluster Survey (HeViCS). The source positions are determined by estimating the likelihood to be a real source for each peak on the maps and the flux densities are estimated using the sourceExtractorTimeline, a timeline-based point source fitter. Afterwards, each source is subtracted from the maps, removing a Gaussian function in every position with the full width half maximum equal to that estimated in sourceExtractorTimeline. This procedure improves the robustness of our algorithm in terms of source identification. The HeViCS catalogs contain about 52000, 42200, and 18700 sources selected at 250, 350, and 500 micron above 3sigma and are ~ 75%, 62%, and 50% complete at flux densities of 20 mJy at 250, 350, 500 micron, respectively. We then measured source number counts at 250, 350, and 500 micron and we also cross-correlated the catalogs with the Sloan Digital Sky Survey to investigate the redshift distribution of the nearby sources. From this cross-correlation, we select ~2000 sources with reliable fluxes and a high signal-to-noise ratio, finding an average redshift z~0.3+/-0.22. The number counts at 250, 350, and 500 micron show an increase in the slope below 200 mJy, indicating a strong evolution in number of density for galaxies at these fluxes. In general, models tend to overpredict the counts at brighter flux densities, underlying the importance of studying the Rayleigh-Jeans part of the spectral energy distribution to refine the theoretical recipes of the models. Our iterative method for source identification allowed the detection of a family of 500 micron sources that are not foreground objects belonging to Virgo and not found in other catalogs.

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arXiv2013

The Herschel Virgo Cluster Survey XIV: transition-type dwarf galaxies in the Virgo cluster

We use dust scaling relations to investigate the hypothesis that Virgo cluster transition-type dwarfs are infalling star-forming field galaxies, which is argued based on their optical features (e.g. disks, spiral arms, bars) and kinematic properties similar to late-type galaxies. After their infall, environmental effects gradually transform them into early-type galaxies through the removal of their interstellar medium and quenching of all star formation activity. In this paper, we aim to verify whether this hypothesis holds using far-infrared diagnostics based on Herschel observations of the Virgo cluster taken as part of the Herschel Virgo Cluster Survey (HeViCS). We select transition-type objects in the nearest cluster, Virgo, based on spectral diagnostics indicative for their residual or ongoing star formation. We detect dust Md ~ 10^{5-6} Msun in 36% of the transition-type dwarfs located on the high end of the stellar mass distribution. This suggests that the dust reservoirs present in non-detections fall just below the Herschel detection limit (< 1.1x10^5 Msun). Dust scaling relations support the hypothesis of a transformation between infalling late-type galaxies to quiescent low-mass spheroids governed by environmental effects, with dust-to-stellar mass fractions for transition-type dwarfs in between values characteristic for late-type objects and the lower dust fractions observed in early-type galaxies. Several transition-type dwarfs demonstrate blue central cores, hinting at the radially outside-in removal of gas and quenching of star formation activity. The fact that dust is also confined to the inner regions suggests that metals are stripped in the outer regions along with the gas. In the scenario of most dust being stripped from the galaxy along with the gas, we argue that... (abridged)

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arXiv2013

Vindicating single-T modified blackbody fits to Herschel SEDs (Research Note)

I show here that the bulk of the dust mass in a galaxy can be equivalently estimated from: i) the full spectral energy distribution of dust emission, using the approach of Draine & Lee (2007) that includes a distribution of dust grains and a range of interstellar radiation field intensities; ii) the emission in the wavelength range 100um <= lambda <= 500um (covered by the Herschel Space Observatory), by fitting to the data a simpler single temperature modified blackbody. Recent claims on the contrary (Dale et al. 2012) should be interpreted as a caveat to use in the simpler fits an absorption cross section which is consistent both in the normalization and in the spectral index beta with that of the full dust model. I also show that the dust mass does not depend significantly on the choice of beta, if both the dust mass and the absorption cross section are derived with the same assumption on beta.

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arXiv2013

The Herschel Virgo Cluster Survey - XIII. Dust in early-type galaxies

Aims. We study the dust content of a large optical input sample of 910 early-type galaxies (ETG) in the Virgo cluster, extending also to the dwarf ETG, and examine the results in relation with those on the other cold ISM components. Methods. We searched for far-infrared emission in all galaxies of the input sample using the 250 micron image of the Herschel Virgo Cluster Survey (HeViCS). This image covers a large fraction of the cluster. For the detected ETG we measured fluxes in 5 bands from 100 to 500 micron, and estimated the dust mass and temperature with modified black-body fits. Results. Dust is detected above the completeness limit of 25.4 mJy at 250 micron in 46 ETG, 43 of which are in the optically complete part of the input sample. In addition dust is present at fainter levels in another 6 ETG. We detect dust in the 4 ETG with synchrotron emission, including M 87. Dust appears to be much more concentrated than stars and more luminous ETG have higher dust temperatures. Dust detection rates down to the 25.4 mJy limit are 17% for ellipticals, about 40% for lenticulars (S0 + S0a) and around 3% for dwarf ETG. Dust mass does not correlate clearly with stellar mass and is often much more than that expected for a passive galaxy in a closed-box model. The dust-to-stars mass ratio anticorrelates with galaxy luminosity, and for some dwarf ETG reaches values as high as for dusty late-type galaxies. In the Virgo cluster slow rotators appear more likely to contain dust than fast ones. Comparing the dust results with those on HI from ALFALFA, there are only 8 ETG detected both in dust and in HI in the HeViCS area; 39 have dust but only an upper limit on HI, and 8 have HI but only an upper limit on dust. The locations of these galaxies in the cluster are different, with the dusty ETG concentrated in the densest regions, while the HI rich ETG are at the periphery.

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arXiv2012

Scaling relations of metallicity, stellar mass, and star formation rate in metal-poor starbursts: I. A fundamental plane

Most galaxies follow well-defined scaling relations of metallicity (O/H), star formation rate (SFR), and stellar mass. However, low-metallicity starbursts, rare in the Local Universe but more common at high redshift, deviate significantly from these scaling relations. On the "main sequence" of star formation, these galaxies have high SFR for a given M*; and on the mass-metallicity relation, they have excess M* for their low metallicity. In this paper, we characterize O/H, M*, and SFR for these deviant "low-metallicity starbursts", selected from a sample of ~1100 galaxies, spanning almost two orders of magnitude in metal abundance, a factor of ~10^6 in SFR, and of ~10^5 in stellar mass. Our sample includes quiescent star-forming galaxies and blue compact dwarfs at redshift 0, luminous compact galaxies at redshift 0.3, and Lyman Break galaxies at redshifts 1-3.4. Applying a Principal Component Analysis (PCA) to the galaxies in our sample with M*<10^{10} Msun gives a Fundamental Plane (FP) of scaling relations; SFR and stellar mass define the plane itself, and O/H its thickness. The dispersion for our sample in the edge-on view of the plane is 0.17 dex, independently of redshift and including the metal-poor starbursts. The same FP is followed by 55100 galaxies selected from the Sloan Digital Sky Survey, with a dispersion of 0.06dex. In a companion paper, we develop multi-phase chemical evolution models that successfully predict the observed scaling relations and the FP; the deviations from the main scaling relations are caused by a different (starburst or "active") mode of star formation. These scaling relations do not truly evolve, but rather are defined by the different galaxy populations dominant at different cosmological epochs.

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arXiv2012

Scaling relations of metallicity, stellar mass, and star formation rate in metal-poor starbursts: II. Theoretical models

Scaling relations of metallicity (O/H), star formation rate (SFR), and stellar mass give important insight on galaxy evolution. They are obeyed by most galaxies in the Local Universe and also at high redshift. In a companion paper, we compiled a sample of ~1100 galaxies from redshift 0 to ~3, spanning almost two orders of magnitude in metal abundance, a factor of $\sim10^6$ in SFR, and of ~10^5 in stellar mass. We have characterized empirically the star-formation "main sequence" (SFMS) and the mass-metallicity relation (MZR) for this sample, and also identified a class of low-metallicity starbursts, rare locally but more common in the distant universe. These galaxies deviate significantly from the main scaling relations, with high SFR and low metal content for a given M*. In this paper, we model the scaling relations and explain these deviations from them with a set of multi-phase chemical evolution models based on the idea that, independently of redshift, initial physical conditions in a galaxy's evolutionary history can dictate its location in the scaling relations. Our models are able to successfully reproduce the O/H, M*, and SFR scaling relations up to z~3, and also successfully predict the molecular cloud fraction as a function of stellar mass. These results suggest that the scaling relations are defined by different modes of star formation: an "active" starburst mode, more common at high redshift, and a quiescent "passive" mode that is predominant locally and governs the main trends.

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arXiv2012

The Herschel Virgo Cluster Survey. XI. Environmental effects on molecular gas and dust in spiral disks

We investigate the dust-to-gas mass ratio and the environmental effects on the various components of the interstellar medium for a spatially resolved sample of Virgo spirals. We have used the IRAM-30m telescope to map over their full extent NGC 4189, NGC 4298, NGC 4388, and NGC 4299 in the 12CO(1-0) and the 12CO(2-1) lines. We observed the same lines in selected regions of NGC 4351, NGC 4294, and NGC 4424. The CO observations are combined with Herschel maps in 5 bands between 100-500 μm from the HeViCS survey, and with HI data from the VIVA survey, to obtain spatially resolved dust and gas distributions. We studied the environmental dependencies by adding to our sample eight galaxies with 12CO(1-0) maps from the literature. We estimate the integrated mass of molecular hydrogen for the galaxies observed in the CO lines. We find molecular-to-total gas mass fractions between 0.04 \leq fmol \leq 0.65, with the lowest values for the dimmest galaxy in the B-band. The integrated dust-to-gas ratio ranges between 0.011 and 0.004. For the 12 mapped galaxies we derive the radial distributions of the atomic gas, molecular gas, and dust. We also study the effect of different CO-to-H2 conversion factors. Both the molecular gas and the dust distributions show steeper radial profiles for HI-deficient galaxies and the average dust-to-gas ratio for these galaxies increases or stays radially constant. On scales of \sim 3 kpc, we find a strong correlation between the molecular gas and the 250 micron surface brightness that is tighter than average for non-deficient galaxies. The correlation becomes linear if we consider the total gas surface mass density. However, the inclusion of atomic hydrogen does not improve the statistical significance of the correlation. The environment can modify the distributions of molecules and dust within a galaxy, although these components are more tightly bound than the atomic gas.

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arXiv2012

The Herschel Virgo Cluster Survey: X.The relationship between cold dust and molecular gas content in Virgo spirals

Using the far-infrared emission, as observed by the Herschel Virgo Cluster Survey (HeViCS), and the integrated HI and CO brightness, we infer the dust and total gas mass for a magnitude limited sample of 35 metal rich spiral galaxies in Virgo. The CO flux correlates tightly and linearly with far-infrared fluxes observed by Herschel. Molecules in these galaxies are more closely related to cold dust rather than to dust heated by star formation or to optical/NIR brightness. We show that dust mass establishes a stronger correlation with the total gas mass than with the atomic or molecular component alone. The dust-to-gas ratio increases as the HI deficiency increases, but in highly HI deficient galaxies it stays constant. Dust is in fact less affected than atomic gas by weak cluster interactions, which remove most of the HI gas from outer and high latitudes regions. Highly disturbed galaxies, in a dense cluster environment, can instead loose a considerable fraction of gas and dust from the inner regions of the disk keeping constant the dust-to-gas ratio. There is evidence that the molecular phase is also quenched. This quencing becomes evident by considering the molecular gas mass per unit stellar mass. Its amplitude, if confirmed by future studies, highlights that molecules are missing in Virgo HI deficient spirals, but to a somewhat lesser extent than dust.

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arXiv2012

The formation of the extremely primitive star SDSS J102915+172927 relies on dust

The relative importance of metals and dust grains in the formation of the first low-mass stars has been a subject of debate. The recently discovered Galactic halo star SDSS J102915+172927 (Caffau et al. 2011) has a mass less than 0.8 Msun and a metallicity of Z = 4.5 10^{-5} Zsun. We investigate the origin and properties of this star by reconstructing the physical conditions in its birth cloud. We show that the observed elemental abundance trend of SDSS J102915+172927 can be well fitted by the yields of core-collapse supernovae with metal-free progenitors of 20 Msun and 35 Msun. Using these selected supernova explosion models, we compute the corresponding dust yields and the resulting dust depletion factor taking into account the partial destruction by the supernova reverse shock. We then follow the collapse and fragmentation of a star forming cloud enriched by the products of these SN explosions at the observed metallicity of SDSS J102915+172927. We find that [0.05 - 0.1] Msun mass fragments, which then lead to the formation of low-mass stars, can occur provided that the mass fraction of dust grains in the birth cloud exceeds 0.01 of the total mass of metals and dust. This, in turn, requires that at least 0.4 Msun of dust condense in the first supernovae, allowing for moderate destruction by the reverse shock. If dust formation in the first supernovae is less efficient or strong dust destruction does occur, the thermal evolution of the SDSS J102915+172927 birth cloud is dominated by molecular cooling, and only > 8 Msun fragments can form. We conclude that the observed properties of SDSS J102915+172927 support the suggestion that dust must have condensed in the ejecta of the first supernovae and played a fundamental role in the formation of the first low-mass stars.

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arXiv2012

Can dust emission be used to map the interstellar medium in high-redshift galaxies? Results from the Herschel Reference Survey

It has often been suggested that an alternative to the standard CO/21-cm method for estimating the mass of the interstellar medium (ISM) in a galaxy might be to estimate the mass of the ISM from the continuum dust emission. In this paper, we investigate the potential of this technique using Herschel observations of ten galaxies in the Herschel Reference Survey and in the Herschel Virgo Cluster Survey. We show that the emission detected by Herschel is mostly from dust that has a temperature and emissivity index similar to that of dust in the local ISM in our galaxy, with the temperature generally increasing towards the centre of each galaxy. We calibrate the dust method using the CO and 21-cm observations to provide an independent estimate of the mass of hydrogen in each galaxy, solving the problem of the uncertain `X factor' for the molecular gas by minimizing the dispersion in the ratio of the masses estimated using the two methods. With the calibration for the dust method and the estimate of the X-factor produced in this way, the dispersion in the ratio of the two gas masses is 30%, which gives an upper limit on the fundamental accuracy of the dust method. The calibration we obtain for the dust method is very similar to an independent Herschel measurement for M31 and to the calibration for the Milky Way from Planck measurements.

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arXiv2011

The first low-mass stars: critical metallicity or dust-to-gas ratio?

We explore the minimal conditions which enable the formation of metal-enriched solar and sub-solar mass stars. We find that in the absence of dust grains, gas fragmentation occurs at densities nH ~ [10^4-10^5]cm^{-3} when the metallicity exceeds Z ~ 10^{-4} Zsun. The resulting fragmentation masses are > 10 Msun. The inclusion of Fe and Si cooling does not affect the thermal evolution as this is dominated by molecular cooling even for metallicities as large as Z = 10^{-2} Zsun. The presence of dust is the key driver for the formation of low-mass stars. We focus on three representative core-collapse supernova (SN) progenitors, and consider the effects of reverse shocks of increasing strength: these reduce the depletion factors, fdep = Mdust/(Mdust+Mmet), alter the shape of the grain size distribution function and modify the relative abundances of grain species and of metal species in the gas phase. We find that the lowest metallicity at which fragmentation occurs is Z=10^{-6} Zsun for gas pre-enriched by the explosion of a 20 Msun primordial SN (fdep > 0.22) and/or by a 35 Msun, Z=10^{-4} Zsun SN (fdep > 0.26); it is ~ 1 dex larger, when the gas is pre-enriched by a Z = 10^{-4} Zsun, 20 Msun SN (fdep > 0.04). Cloud fragmentation depends on the depletion factor and it is suppressed when the reverse shock leads to a too large destruction of dust grains. These features are all consistent with the existence of a minimum dust-to-gas ratio, Dcr, above which fragmentation is activated. We derive a simple analytic expression for Dcr which, for grain composition and properties explored in the present study, reads Dcr = [2.6 - 6.3] x 10^{-9}. When the dust-to-gas ratio of star forming clouds exceeds this value, the fragmentation masses range between 0.01 Msun and 1 Msun, thus enabling the formation of the first low-mass stars.

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arXiv2011

The extent of dust in NGC 891 from Herschel/SPIRE images

We analyse Herschel/SPIRE images of the edge-on spiral galaxy NGC 891 at 250, 350 and 500 micron. Using a 3D radiative transfer model we confirm that the dust has a radial fall-off similar to the stellar disk. The dust disk shows a break at about 12 kpc from the center, where the profile becomes steeper. Beyond this break, emission can be traced up to 90% of the optical disk in the NE side. On the SW, we confirm dust emission associated with the extended, asymmetric HI disk, previously detected by the Infrared Space Observatory (ISO). This emission is marginally consistent with the large diffuse dust disk inferred from radiative transfer fits to optical images. No excess emission is found above the plane beyond that of the thin, unresolved, disk.

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arXiv2011

The origin of dust in high redshift QSOs: the case of SDSS J1148+5251

We present a semi-analytical model for the formation and evolution of a high redshift quasar (QSO). We reconstruct a set of hierarchical merger histories of a 10^13 Msun dark matter halo and model the evolution of the corresponding galaxy and of its central super massive black hole. The code GAMETE/QSODUST consistently follows: the black hole assembly via both coalescence with other black holes and gas accretion; the build up and star formation history of the quasar host galaxy, driven by binary mergers and mass accretion; the evolution of gas, stars, metals in the interstellar medium (ISM), accounting for mass exchanges with the external medium (infall and outflow processes); dust formation in Supernova (SN) ejecta and in the stellar atmosphere of Asymptotic Giant Branch (AGB) stars, dust destruction by interstellar shocks and grain growth in molecular clouds; the AGN feedback which powers a galactic-scale wind, self-regulating the black hole growth and eventually halting star formation.We use this model to study the case of SDSS J1148+5251 observed at redshift 6.4, exploring different star formation histories for the QSO host galaxy.

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arXiv2011

The Herschel Virgo Cluster Survey. IX. Dust-to-gas mass ratio and metallicity gradients in four Virgo spiral galaxies

Using Herschel data from the Open Time Key Project the Herschel Virgo Cluster Survey (HeViCS), we investigated the relationship between the metallicity gradients expressed by metal abundances in the gas phase as traced by the chemical composition of HII regions, and in the solid phase, as traced by the dust-to-gas mass ratio. We derived the radial gradient of the dust-to-gas mass ratio for all galaxies observed by HeViCS whose metallicity gradients are available in the literature. They are all late type Sbc galaxies, namely NGC4254, NGC4303, NGC4321, and NGC4501. We examined different dependencies on metallicity of the CO-to-H$_2$ conversion factor (\xco), used to transform the $^{12}$CO observations into the amount of molecular hydrogen. We found that in these galaxies the dust-to-gas mass ratio radial profile is extremely sensitive to choice of the \xco\ value, since the molecular gas is the dominant component in the inner parts. We found that for three galaxies of our sample, namely NGC4254, NGC4321, and NGC4501, the slopes of the oxygen and of the dust-to-gas radial gradients agree up to $\sim$0.6-0.7R$_{25}$ using \xco\ values in the range 1/3-1/2 Galactic \xco. For NGC4303 a lower value of \xco$\sim0.1\times$ 10$^{20}$ is necessary. We suggest that such low \xco\ values might be due to a metallicity dependence of \xco (from close to linear for NGC4254, NGC4321, and NGC4501 to superlinear for NGC4303), especially in the radial regions R$_G<$0.6-0.7R$_{25}$ where the molecular gas dominates. On the other hand, the outer regions, where the atomic gas component is dominant, are less affected by the choice of \xco, and thus we cannot put constraints on its value.

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