arXiv subjects

S. Salvadori

Publications and source records attributed to S. Salvadori.

35 records · Page 2Linked to original sources

arXiv2017

The impact of chemistry on the structure of high-z galaxies

To improve our understanding of high-z galaxies we study the impact of H$_{2}$ chemistry on their evolution, morphology and observed properties. We compare two zoom-in high-resolution (30 pc) simulations of prototypical $M_{\star}\sim 10^{10} {\rm M}_{\odot}$ galaxies at $z=6$. The first, "Dahlia", adopts an equilibrium model for H$_{2}$ formation, while the second, "Althæa", features an improved non-equilibrium chemistry network. The star formation rate (SFR) of the two galaxies is similar (within 50\%), and increases with time reaching values close to 100 ${\rm M}_{\odot}/\rm yr$ at $z=6$. They both have SFR-stellar mass relation consistent with observations, and a specific SFR of $\simeq 5\, {\rm Gyr}^{-1}$. The main differences arise in the gas properties. The non-equilibrium chemistry determines the H$\rightarrow$ H$_{2}$~transition to occur at densities $> 300\,{cm}^{-3}$, i.e. about 10 times larger than predicted by the equilibrium model used for Dahlia. As a result, Althæa features a more clumpy and fragmented morphology, in turn making SN feedback more effective. Also, because of the lower density and weaker feedback, Dahlia sits $3σ$ away from the Schmidt-Kennicutt relation; Althæa, instead nicely agrees with observations. The different gas properties result in widely different observables. Althæa outshines Dahlia by a factor of 7 (15) in [CII]~$157.74\,μ{\rm m}$ (H$_{2}$~$17.03\,μ{\rm m}$) line emission. Yet, Althæa is under-luminous with respect to the locally observed [CII]-SFR relation. Whether this relation does not apply at high-z or the line luminosity is reduced by CMB and metallicity effects remains as an open question.

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arXiv2017

The Gaia-ESO Survey: Galactic evolution of sulphur and zinc

Due to their volatile nature, when sulfur and zinc are observed in external galaxies, their determined abundances represent the gas-phase abundances in the interstellar medium. This implies that they can be used as tracers of the chemical enrichment of matter in the Universe at high redshift. Comparable observations in stars are more difficult and, until recently, plagued by small number statistics. We wish to exploit the Gaia ESO Survey (GES) data to study the behaviour of sulfur and zinc abundances of a large number of Galactic stars, in a homogeneous way. By using the UVES spectra of the GES sample, we are able to assemble a sample of 1301 Galactic stars, including stars in open and globular clusters in which both sulfur and zinc were measured. We confirm the results from the literature that sulfur behaves as an alpha-element. We find a large scatter in [Zn/Fe] ratios among giant stars around solar metallicity. The lower ratios are observed in giant stars at Galactocentric distances less than 7.5 kpc. No such effect is observed among dwarf stars, since they do not extend to that radius. Given the sample selection, giants and dwarfs are observed at different Galactic locations, and it is plausible, and compatible with simple calculations, that Zn-poor giants trace a younger population more polluted by SN Ia yields. It is necessary to extend observations in order to observe both giants and dwarfs at the same Galactic location. Further theoretical work on the evolution of zinc is also necessary.

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arXiv2017

The history of the dark and luminous side of Milky Way-like progenitors

Here we investigate the evolution of a Milky Way (MW) -like galaxy with the aim of predicting the properties of its progenitors all the way from $z \sim 20$ to $z = 0$. We apply GAMESH (Graziani et al. 2015) to a high resolution N-Body simulation following the formation of a MW-type halo and we investigate its properties at $z \sim 0$ and its progenitors in $0 < z < 4$. Our model predicts the observed galaxy main sequence, the mass-metallicity and the fundamental plane of metallicity relations in $0 < z < 4$. It also reproduces the stellar mass evolution of candidate MW progenitors in $0 \lesssim z \lesssim 2.5$, although the star formation rate and gas fraction of the simulated galaxies follow a shallower redshift dependence. We find that while the MW star formation and chemical enrichment are dominated by the contribution of galaxies hosted in Lyman $α$-cooling halos, at z > 6 the contribution of star forming mini-halos is comparable to the star formation rate along the MW merger tree. These systems might then provide an important contribution in the early phases of reionization. A large number of mini-halos with old stellar populations, possibly Population~III stars, are dragged into the MW or survive in the Local Group. At low redshift dynamical effects, such as halo mergers, tidal stripping and halo disruption redistribute the baryonic properties among halo families. These results are critically discussed in light of future improvements including a more sophisticated treatment of radiative feedback and inhomogeneous metal enrichment.

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arXiv2016

Zooming on the internal structure of $z\simeq6$ galaxies

We present zoom-in, AMR, high-resolution ($\simeq 30$ pc) simulations of high-redshift ($z \simeq 6$) galaxies with the aim of characterizing their internal properties and interstellar medium. Among other features, we adopt a star formation model based on a physically-sound molecular hydrogen prescription, and introduce a novel scheme for supernova feedback, stellar winds and dust-mediated radiation pressure. In the zoom-in simulation the target halo hosts "Dahlia", a galaxy with a stellar mass $M_*=1.6\times 10^{10}$M$_\odot$, representative of a typical $z\sim 6$ Lyman Break Galaxy. Dahlia has a total H2 mass of $10^{8.5}$M$_\odot$, that is mainly concentrated in a disk-like structure of effective radius $\simeq 0.6$ kpc and scale height $\simeq 200$ pc. Frequent mergers drive fresh gas towards the center of the disk, sustaining a star formation rate per unit area of $\simeq 15 $M$_\odot$ yr$^{-1}$ kpc$^{-2}$. The disk is composed by dense ($n \gtrsim 25$ cm$^{-3}$), metal-rich ($Z \simeq 0.5 $ Z$_\odot$) gas, that is pressure-supported by radiation. We compute the $158μ$m [CII] emission arising from {Dahlia}, and find that $\simeq 95\%$ of the total [CII] luminosity ($L_{[CII]}\simeq10^{7.5}$ L$_\odot$) arises from the H2 disk. Although $30\%$ of the CII mass is transported out of the disk by outflows, such gas negligibly contributes to [CII] emission, due to its low density ($n \lesssim 10$ cm$^{-3}$) and metallicity ($Z\lesssim 10^{-1}$Z$_\odot$). Dahlia is under-luminous with respect to the local [CII]-SFR relation; however, its luminosity is consistent with upper limits derived for most $z\sim6$ galaxies.

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arXiv2016

Limits on Pop III star formation with the most iron-poor stars

We study the impact of star-forming mini-haloes, and the Initial Mass Function (IMF) of Population III (Pop III) stars, on the Galactic halo Metallicity Distribution Function (MDF) and on the properties of C-enhanced and C-normal stars at [Fe/H]<-3. For our investigation we use a data-constrained merger tree model for the Milky Way formation, which has been improved to self-consistently describe the physical processes regulating star-formation in mini-haloes, including the poor sampling of the Pop III IMF. We find that only when star-forming mini-haloes are included the low-Fe tail of the MDF is correctly reproduced, showing a plateau that is built up by C-enhanced metal-poor (CEMP) stars imprinted by primordial faint supernovae. The incomplete sampling of the Pop III IMF in inefficiently star-forming mini-haloes (< $10^{-3}$ $M_\odot$/yr) strongly limits the formation of Pair Instability Supernovae (PISNe), with progenitor masses $m_{\rm popIII}$=[140-260] $M_\odot$, even when a flat Pop III IMF is assumed. Second-generation stars formed in environments polluted at >50% level by PISNe are thus extremely rare, corresponding to $\approx$ 0.25% of the total stellar population at [Fe/H]<-2, which is consistent with recent observations. The low-Fe tail of the MDF strongly depends on the Pop III IMF shape and mass range. Given the current statistics, we find that a flat Pop III IMF model with $m_{\rm popIII}$=[10-300] $M_\odot$ is disfavoured by observations. We present testable predictions for Pop III stars extending down to lower masses, with $m_{\rm popIII}$=[0.1-300] $M_\odot$.

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arXiv2016

TOPoS: III. An ultra iron-poor multiple CEMP system

One of the primary objectives of the TOPoS survey is to search for the most metal-poor stars. Our search has led to the discovery of one of the most iron-poor objects known, SDSS\,J092912.32+023817.0. This object is a multiple system, in which two components are clearly detected in the spectrum. We have analysed 16 high-resolution spectra obtained using the UVES spectrograph at the ESO 8.2m VLT telescope to measure radial velocities and determine the chemical composition of the system. Cross correlation of the spectra with a synthetic template yields a double-peaked cross-correlation function (CCF) for eight spectra, and in one case there is evidence for the presence of a third peak. Chemical analysis of the spectrum obtained by averaging all the spectra for which the CCF showed a single peak found that the iron abundance is [Fe/H]=-4.97. The system is also carbon enhanced with [C/Fe]=+3.91 (A(C)=7.44). From the permitted oxygen triplet we determined an upper limit for oxygen of [O/Fe]<+3.52 such that C/O>1.3. We are also able to provide more stringent upper limits on the Sr and Ba abundances ([Sr/Fe]<+0.70, and [Ba/Fe]<+1.46, respectively).

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arXiv2015

The Brightest Ly$α$ Emitter: Pop III or Black Hole?

CR7 is the brightest $z=6.6 \, {\rm Ly}α$ emitter (LAE) known to date, and spectroscopic follow-up by Sobral et al. (2015) suggests that CR7 might host Population (Pop) III stars. We examine this interpretation using cosmological hydrodynamical simulations. Several simulated galaxies show the same "Pop III wave" pattern observed in CR7. However, to reproduce the extreme CR7 ${\rm Ly}α$/HeII1640 line luminosities ($L_{\rm α/He II}$) a top-heavy IMF and a massive ($>10^{7}{\rm M}_{\odot}$) PopIII burst with age $<2$ Myr are required. Assuming that the observed properties of ${\rm Ly}α$ and HeII emission are typical for Pop III, we predict that in the COSMOS/UDS/SA22 fields, 14 out of the 30 LAEs at $z=6.6$ with $L_α >10^{43.3}{\rm erg}\,{\rm s}^{-1}$ should also host Pop III stars producing an observable $L_{\rm He II}>10^{42.7}{\rm erg}\,{\rm s}^{-1}$. As an alternate explanation, we explore the possibility that CR7 is instead powered by accretion onto a Direct Collapse Black Hole (DCBH). Our model predicts $L_α$, $L_{\rm He II}$, and X-ray luminosities that are in agreement with the observations. In any case, the observed properties of CR7 indicate that this galaxy is most likely powered by sources formed from pristine gas. We propose that further X-ray observations can distinguish between the two above scenarios.

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arXiv2015

The ACS LCID Project: On the origin of dwarf galaxy types: a manifestation of the halo assembly bias?

We discuss how knowledge of the whole evolutionary history of dwarf galaxies, including details on the early star formation events, can provide insight on the origin of the different dwarf galaxy types. We suggest that these types may be imprinted by the early conditions of formation rather than being only the result of a recent morphological transformation driven by environmental effects. We present precise star formation histories of a sample of Local Group dwarf galaxies, derived from colour-magnitude diagrams reaching the oldest main-sequence turnoffs. We argue that these galaxies can be assigned to two basic types: fast dwarfs that started their evolution with a dominant and short star formation event, and slow dwarfs that formed a small fraction of their stars early and have continued forming stars until the present time (or almost). These two different evolutionary paths do not map directly onto the present-day morphology (dwarf spheroidal vs dwarf irregular). Slow and fast dwarfs also differ in their inferred past location relative to the Milky Way and/or M31, which hints that slow dwarfs were generally assembled in lower density environments than fast dwarfs. We propose that the distinction between a fast and slow dwarf galaxy reflects primarily the characteristic density of the environment where they form. At a later stage, interaction with a large host galaxy may play a role in the final gas removal and ultimate termination of star formation.

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arXiv2015

Galaxy formation with radiative and chemical feedback

Here we introduce GAMESH, a novel pipeline which implements self-consistent radiative and chemical feedback in a computational model of galaxy formation. By combining the cosmological chemical-evolution model GAMETE with the radiative transfer code CRASH, GAMESH can post process realistic outputs of a N-body simulation describing the redshift evolution of the forming galaxy. After introducing the GAMESH implementation and its features, we apply the code to a low-resolution N-body simulation of the Milky Way formation and we investigate the combined effects of self-consistent radiative and chemical feedback. Many physical properties, which can be directly compared with observations in the Galaxy and its surrounding satellites, are predicted by the code along the merger-tree assembly. The resulting redshift evolution of the Local Group star formation rates, reionisation and metal enrichment along with the predicted Metallicity Distribution Function of halo stars are critically compared with observations. We discuss the merits and limitations of the first release of GAMESH, also opening new directions to a full implementation of feedback processes in galaxy formation models by combining semi-analytic and numerical methods.

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arXiv2014

Initial mass function of intermediate mass black hole seeds

We study the Initial Mass Function (IMF) and host halo properties of Intermediate Mass Black Holes (IMBH, 10^{4-6} Msun) formed inside metal-free, UV illuminated atomic cooling haloes (virial temperature T_vir > 10^4 K) either via the direct collapse of the gas or via an intermediate Super Massive Star (SMS) stage. We achieve this goal in three steps: (a) we derive the gas accretion rate for a proto-SMS to undergo General Relativity instability and produce a direct collapse black hole (DCBH) or to enter the ZAMS and later collapse into a IMBH; (b) we use merger-tree simulations to select atomic cooling halos in which either a DCBH or SMS can form and grow, accounting for metal enrichment and major mergers that halt the growth of the proto-SMS by gas fragmentation. We derive the properties of the host halos and the mass distribution of black holes at this stage, and dub it the "Birth Mass Function"; (c) we follow the further growth of the DCBH due to accretion of leftover gas in the parent halo and compute the final IMBH mass.We consider two extreme cases in which minihalos (T_vir < 10^4 K) can (fertile) or cannot (sterile) form stars and pollute their gas leading to a different IMBH IMF. In the (fiducial) fertile case the IMF is bimodal extending over a broad range of masses, M= (0.5-20)x10^5 Msun, and the DCBH accretion phase lasts from 10 to 100 Myr. If minihalos are sterile, the IMF spans the narrower mass range M= (1-2.8)x10^6 Msun, and the DCBH accretion phase is more extended (70-120 Myr). We conclude that a good seeding prescription is to populate halos (a) of mass 7.5 < log (M_h/Msun) < 8, (b) in the redshift range 8 < z < 17, (c) with IMBH in the mass range 4.75 < log (M_BH/Msun) < 6.25.

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arXiv2014

Simulating cosmic metal enrichment by the first galaxies

We study cosmic metal enrichment via AMR hydrodynamical simulations in a (10 Mpc/h)$^3$ volume following the Pop III-Pop II transition and for different Pop III IMFs. We have analyzed the joint evolution of metal enrichment on galactic and intergalactic scales at z=6 and z=4. Galaxies account for <9% of the baryonic mass; the remaining gas resides in the diffuse phases: (a) voids, i.e. regions with extremely low density ($Δ$<1), (b) the true intergalactic medium (IGM, 1<$Δ$<10) and (c) the circumgalactic medium (CGM, 10<$Δ<10^{2.5}$), the interface between the IGM and galaxies. By z=6 a galactic mass-metallicity relation is established. At z=4, galaxies with a stellar mass $M_*=10^{8.5}M_\odot$ show log(O/H)+12=8.19, consistent with observations. The total amount of heavy elements rises from $Ω^{SFH}_Z=1.52\, 10^{-6}$ at z=6 to 8.05 $10^{-6}$ at z=4. Metals in galaxies make up to ~0.89 of such budget at z=6; this fraction increases to ~0.95 at z=4. At z=6 (z=4) the remaining metals are distributed in CGM/IGM/voids with the following mass fractions: 0.06/0.04/0.01 (0.03/0.02/0.01). Analogously to galaxies, at z=4 a density-metallicity ($Δ$-Z) relation is in place for the diffuse phases: the IGM/voids have a spatially uniform metallicity, Z~$10^{-3.5}$Zsun; in the CGM Z steeply rises with density up to ~$10^{-2}$Zsun. In all diffuse phases a considerable fraction of metals is in a warm/hot (T>$10^{4.5}$K) state. Due to these physical conditions, CIV absorption line experiments can probe only ~2% of the total carbon present in the IGM/CGM; however, metal absorption line spectra are very effective tools to study reionization. Finally, the Pop III star formation history is almost insensitive to the chosen Pop III IMF. Pop III stars are preferentially formed in truly pristine (Z=0) gas pockets, well outside polluted regions created by previous star formation episodes.

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arXiv2013

Metals and ionizing photons from dwarf galaxies

We estimate the potential contribution of M < 10^9 Msun dwarf galaxies to the reionization and early metal-enrichment of the Milky Way environment, or circum-Galactic Medium. Our approach is to use the observed properties of ancient stars (> 12 Gyr old) measured in nearby dwarf galaxies to characterize the star-formation at high-z. We use a merger-tree model for the build-up of the Milky Way, which self-consistently accounts for feedback processes, and which is calibrated to match the present-day properties of the Galaxy and its dwarf satellites. We show that the high-z analogues of nearby dwarf galaxies can produce the bulk of ionizing radiation (>80%) required to reionize the Milky Way environment. Our fiducial model shows that the gaseous environment can be 50% reionized at z ~ 8 by galaxies with 10^7 Msun < M < 10^8 Msun. At later times, radiative feedback stops the star-formation in these small systems, and reionization is completed by more massive dwarf galaxies by z_rei = 6.4\pm 0.5. The metals ejected by supernova-driven outflows from M < 10^9 Msun dwarf galaxies almost uniformly fill the Milky Way environment by z ~ 5, enriching it to Z ~ 2 10^-2 Zsun. At z ~ 2 these early metals are still found to represent ~ 50% of the total mass of heavy elements in the circum-Galactic Medium.

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arXiv2011

VLT/FLAMES spectroscopy of Red Giant Branch stars in the Carina dwarf spheroidal galaxy

The ages of individual Red Giant Branch stars (RGB) can range from 1 Gyr old to the age of the Universe, and it is believed that the abundances of most chemical elements in their photospheres remain unchanged with time (those that are not affected by the 1st dredge-up). This means that they trace the ISM in the galaxy at the time the star formed, and hence the chemical enrichment history of the galaxy. CMD analysis has shown the Carina dwarf spheroidal (dSph) to have had an unusually episodic star formation history (SFH) which is expected to be reflected in the abundances of different chemical elements. We use the VLT-FLAMES spectrograph in HR mode (R~20000) to measure the abundances of several chemical elements in a sample of 35 RGB stars in Carina. We also combine these abundances with photometry to derive age estimates for these stars. This allows us to determine which of two distinct star formation (SF) episodes the stars in our sample belong to, and thus to define the relationship between SF and chemical enrichment during these two episodes. As is expected from the SFH, Carina contains two distinct populations of RGB stars: one old (>10 Gyr), which we have found to be metal-poor ([Fe/H]<-1.5), and alpha-rich ([Mg/Fe]>0.0); the other intermediate age (~2-6 Gyr), which we have found to have a metallicity range (-1.8<[Fe/H]<-1.2) with a large spread in [alpha/Fe] abundance, going from extremely low values ([Mg/Fe]<-0.3) to the same mean values as the older population (<[Mg/Fe]>~0.3). We show that the chemical enrichment history of the Carina dSph was different for each SF episode. The earliest was short (~2-3 Gyr) and resulted in the rapid chemical enrichment of the whole galaxy to [Fe/H] ~ -1.5 with both SNe II and SNe Ia contributions. The subsequent episode occured after a gap of ~3-4 Gyr and appears to have resulted in relatively little evolution in either [Fe/H] or [alpha/Fe].

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arXiv2010

High redshift Lya emitters: clues on the Milky Way infancy

With the aim of determining if Milky Way (MW) progenitors could be identified as high redshift Lyman Alpha Emitters (LAEs) we have derived the intrinsic properties of z ~ 5.7 MW progenitors, which are then used to compute their observed Lyman-alpha luminosity, L_alpha, and equivalent width, EW. MW progenitors visible as LAEs are selected according to the canonical observational criterion, L_alpha > 10^42 erg/s and EW > 20 A. Progenitors of MW-like galaxies have L_alpha = 10^(39-43.25) erg/s, making some of them visible as LAEs. In any single MW merger tree realization, typically only 1 (out of ~ 50) progenitor meets the LAE selection criterion, but the probability to have at least one LAE is very high, P = 68%. The identified LAE stars have ages, t_* ~ 150-400 Myr at z ~ 5.7 with the exception of five small progenitors with t_* < 5 Myr and large EW = 60-130 A. LAE MW progenitors provide > 10% of the halo very metal-poor stars [Fe/H] < -2, thus establishing a potentially fruitful link between high-z galaxies and the Local Universe.

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arXiv2010

Mining the Galactic Halo for Very Metal-Poor Stars

We study the age and metallicity distribution function (MDF) of metal-poor stars in the Milky Way halo as a function of galactocentric radius by combining N-body simulations and semi-analytical methods. We find that the oldest stars populate the innermost region, while extremely metal-poor stars are more concentrated within r < 60 kpc. The MDF of [Fe/H] < -2 stars varies only very weakly within the central 50 kpc, while the relative contribution of [Fe/H] < -2 stars strongly increases with r, varying from 16% within 7 kpc < r < 20 kpc up to > 40% for r > 20 kpc. This is due to the faster descent of the spatial distribution (as seen from Earth) of the more enriched population. This implies that the outer halo < 40 kpc is the best region to search for very metal-poor stars. Beyond ~ 60 kpc the density of [Fe/H] < -2 stars is maximum within dwarf galaxies. All these features are imprinted by a combination of (i) the virialization epoch of the star-forming haloes, and (ii) the metal enrichment history of the Milky Way environment.

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arXiv2008

Life and times of dwarf spheroidal galaxies

We propose a cosmological scenario for the formation and evolution of dwarf spheroidal galaxies (dSphs), satellites of the Milky Way (MW). An improved version of the semi-analytical code GAMETE (GAlaxy Merger Tree & Evolution) is used to follow the dSphs evolution simultaneously with the MW formation, matching the observed properties of both. In this scenario dSph galaxies represent fossil objects virializing at z = 7.2 +/- 0.7 (i.e. in the pre-reionization era z > z_rei = 6) in the MW environment, which at that epoch has already been pre-enriched up to [Fe/H] ~ -3; their dynamical masses are in the narrow range M = (1.6 +/- 0.7) x 10^8 M_sun, although a larger spread might be introduced by a more refined treatment of reionization. Mechanical feedback effects are dramatic in such low-mass objects, causing the complete blow-away of the gas ~100 Myr after the formation epoch: 99% of the present-day stellar mass, M_* = (3 +/- 0.7) x 10^6 M_sun, forms during this evolutionary phase, i.e. their age is >13 Gyr. Later on, star formation is re-ignited by returned gas from evolved stars and a second blow-away occurs. The cycle continues for about 1 Gyr during which star formation is intermittent. At z = 0 the dSph gas content is M_g = (2.68 +/- 0.97) x 10^4 M_sun. Our results match several observed properties of Sculptor, used as a template of dSphs: (i) the Metallicity Distribution Function; (ii) the Color Magnitude Diagram; (iii) the decrement of the stellar [O/Fe] abundance ratio for [Fe/H] > -1.5; (iv) the dark matter content and the light-to-mass ratio; (v) the HI gas mass content.

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arXiv2007

Cosmic stellar relics in the Galactic halo

We study the stellar population history and chemical evolution of the Milky Way (MW) in a hierarchical LCDM model for structure formation. Using a Monte Carlo method based on the semi-analytical EPS formalism, we reconstruct the merger tree of our Galaxy and follow the evolution of gas and stars along the hierarchy. Our approach allows us to compare the observational properties of the MW with model results, exploring different properties of primordial stars, such as their IMF and the critical metallicity for low-mass star formation, Zcr. By matching our predictions to the Metallicity Distribution Function (MDF) of metal-poor stars in the Galactic halo we find that: (i) supernova feedback is required to reproduce the observed properties of the MW; (ii) stars with [Fe/H]<-2.5 form in halos accreting Galactic Medium (GM) enriched by earlier supernova explosions; (iii) the fiducial model (Zcr=10^-4Zsun,m_PopIII=200Msun) provides an overall good fit to the MDF but cannot account for the two stars with [Fe/H]<-5; the latter can be accommodated if Zcr<10^-6Zsun but such model overpopulates the range -5.3<[Fe/H]<-4 in which no stars have been detected; (iv) the current non-detection of metal-free stars robustly constrains either Zcr>0 or the masses of the first stars m_PopIII>0.9Msun; (v) the statistical impact of second generation stars, i.e stars forming out of gas polluted only by metal-free stars, is negligible in current samples; (vi) independently of Zcr, 60% of metals in the GM are ejected through winds by halos with masses M<6x10^9 Msun, showing that low-mass halos are the dominant population contributing to cosmic metal enrichment.

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