# Presentation: 683793

## Cosmic stellar relics in the Galactic halo

**Cosmic stellar relics in the Galactic halo**

**Stefania Salvadori****1****, Raffaella Schneider****2**** & Andrea Ferrara****1**
** ***1**SISSA/International School for Advanced Studies, via Beirut 4, 34100 Trieste, Italy  *
*  **2**INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy*

**The model**** **

*[1]Cole S. et al., 2000 MNRAS, 319, 168. [2]Volonteri M., Haardt F. & Madau P., 2003, ApJ, 582, 559. [3]Bromm et al., 2001, MNRAS, 328, 969. [4]Omukai K., 2001, ApJ, 534, 809.  [5]Omukai K. et al., 2005, ApJ, 626, 627. [6]Schneider R. et al., 2002, ApJ, 571, 30. [7]Schneider et al., 2003, Nat, 422, 869.  [8]Schneider et al., 2006, MNRAS, 369, 1437. [9]Bromm V. & Loeb A., 2004, New Astron., 9, 353. [10]Ganguly R. et al., 2005, ApJ, 157, 251.*
*[11]Mori M. & Umemura M., 2006, Nat, 440, 644. [12]Beers & Christlieb 2006, private communication. [13]Christlieb N. et al., 2002, Nat, 419, 904. [14]Frebel A.. et al., 2005, Nat. 434, 871. [15]Christlieb N., Bessel M. & Eriksson K., 2006, in preparation*

- Metal poor stars represent the living fossils of the first stellar generations. The Metallicity Distribution Function (MDF) of long living metal poor stars is observed both in the Galactic halo and in nearby dwarf galaxies, satellites of the Milky Way (MW). Using a Monte Carlo method based on the semi-analytical Press & Schechter formalism, we develop a new code GAMETE (GAlaxy MErger Tree & Evolution) to reconstruct the merger tree of the Galaxy and follow the evolution of gas and stars along the hierarchical tree. Our approach allows to compare the observational properties of the MW with model results exploring the imprint of undetectable high redshift processes. By matching model predictions to the observed MDF of metal poor stars in the Galactic halo we: *(i)* study the metal enrichment history of the MW environment; *(ii)* set limits on the primordial Initial Mass Function (IMF) and the critical metallicity (Zcr) governing the transition from PopIII to PopII star formation mode; *(iii)* investigate the statistical impact of second generation of stars in up-to-date observed samples.

**Hierarchical merger tree:**
- Along the lines of Cole ([1]) and Volonteri, Haardt  & Madau ([2]) we have developed a binary Monte Carlo algorithm with accretion mass in order to reconstruct the hierarchical merger tree of the Galaxy up to z=20. At each time-step halos can lose part of their mass (corresponding to a cumulative fragmentation into halos with M<Mres) or lose mass and fragment into two progenitor halos. We have assumed a mass resolution Mres= M4(z)/10, where M4(z) represents the halo mass which corresponds to a virial equilibrium temperature Tvir=104K. At each redshift the mass below the resolution limit accounts for  the Galactic Medium (GM) which represents the mass reservoir into which halos are embedded.

**Star formation history:**
- Several simple but physically motivated prescriptions have been adopted in order to study the star formation history & the chemical evolution along the hierarchical tree:
- (i) Stars form in Lyα cooling halos (Tvir > 104K )
- (ii) M* = f*(z) Mgas= ε* Δt/tff(z) Mgas where tff is the free-fall time and ε* a free parameter
- (iii) According to the critical metallicity scenario ([3,4,5,6,7,8,9])  low-mass star formation is triggered by the presence of metals in the gas exceeding Zcr=10-5±1Z :
-     PopIII stars form if  Z ≤ Zcr and with a reference mass mPopIII = 200 M
-     PopII/I stars form if  Z > Zcr and according to a Salpeter IMF (0.1 M< m* < 100 M)
- (iv) Stars, once formed, evolve instantaneously (IRA approximation)
- (v) Mechanical feedback is active if SN explosion energy ESN= εwNSN<ESN> overcomes the  binding energy of  the halo. εw is the second free parameter of the model
- (vi) Gas & metals ejected into the Interstellar Medium (ISM), an eventually into the GM through mechanical feedback, are instantaneously & homogeneously mixed in it.

**Model Calibration:**
- We have used the observed properties of the MW to fix the best values of the two model free parameters, ε* and εw which respectively regulate the star formation and the wind efficiency. We found that the calibration procedure is completely independent of Zcr and PopIII IMF.
*The global properties of the MW are well reproduced both using a close-box model (**ε*****=0.5, ε**w**=0 .i.e. no wind**) and a model including mechanical feedback (**ε*****=0.7,ε**w **=0.2**).*

**The Metallicity Distribution Function:**
- We use the properties of the MDF in order to study the role of feedback and discriminate between the two best fit models (Fig.1). Close box models do not reproduce the observed [Fe/H] range since no stars with [Fe/H] ≤ -1.6 are formed. Feedback models instead allow an efficient dilution of metals. Low-[Fe/H] PopII stars form in halos accreting GM gas enriched by earlier SN explosion (Fig.2a).
-  *Mechanical feedback is required in order to  reproduce both the global properties of the MW and the observed [Fe/H] range*. We refer to the case ε*=0.7, εw=0.2 as our fiducial model.

**Model results**

- Fig.1 : MDFs for  models  ε = 0.5, εw= 0 (shaded  histogram) and  ε*= 0.7,, εw= 0.2 (no shaded  histogram)  Histograms are obtained as average over 200 realizations.of the merger tree

**Z****cr****=10****–****4 ****Z********   ****m****PopIII ****= 200 M******

- Observed [Fe/H ] range

**The Galactic Medium:**
- We study the evolution of  GM iron and oxygen abundance together with the specific contribution to [O/H] by PopIII and PopII stars (Fig.2a). We find that *PopIII stars dominate the GM enrichment for 11 < z < 20 while PopII stars are the dominant enrichment channel at lower redshifts z < 11. The 60% of the total amount of metals predicted in the GM at z=0 have been ejected by halos with* M ≤ 6·109M (Fig.2b)

- Fig.2a: Evolution of the GM elemental abundances. Solid lines show the [Fe/H] and [O/H] evolution averaged over 200 realization. The shaded area delimits the ±σ dispersion region for [Fe/H]. The point is the measured [O/H] in High velocity clouds ([10]). Fig.2b: *Lower panel*: ratio of metals ejected by halos (Mej ) as a function of their mass and redshift with respect to the total amount of metals predicted in the GM at z=0 (MejTOT ). Curves represent Mej/MejTOT=5·10–(4,3,2) isocontour. The minimum and maximum (Mmin ,Mmax) halo mass in which star formation can develop are also shown. The two rectangles identify the position of the maxima; the horizontal line show the PopIII stars termination epoch.*Top panel*: the shaded area shows the cumulative contribution to MejTOT , integrated over redshift, by halos with different mass; points with associated ±1σ error bars represent stellar-to-total mass ratios in the corresponding mass bin.

**Comparison with data**

**The fiducial Model:**
- We compare the new MDF determination for Galactic halo stars by Beers & Christlieb ([12]) with the simulated MDF obtained using the fiducial model (Fig.3).  For completeness we have added to the sample the two known hyper-metal poor stars (HMPS) ([13,14,15]).
*The fiducial model provide a good fit to the MDF but cannot account for the two HMPS.** *

- Fig.3 :  *Left panel: * MDFs observed  (points, [3]) and  simulated (histogram) using  the fiducial model and Zcr=10–4 Z,  mPopIII =200M.  The histogram represents the average value of the MDF over 200  realizations of the merger tree; the shaded area the ±σ Poissonian errors. *Right panel*: The same results plotted  in terms of cumulative number of stars below a given [Fe/H]

**Constraints on Z****cr**** value:**
- We explore the sensitivity of our results to variation of Zcr  (Fig.4). The choice Zcr=0 is equivalent to state that stars, including metal-free ones, form at all times according to a Salpeter IMF. *Models with Z**cr **≤ 10**-6 **Z**** **can account for the two HMP stars at the price of overpopulating the “metallicity desert” – 5.3 < [Fe/H] < – 4*

- Fig.5 : The same as Fig.3 but for values of Zcr=10–5 , 10–6 , 0.

**Statistics of second generation stars:**
- We study, for different Zcr models, the statistical impact of  “second generation” (2G) stars i.e. stars that form out of gas enriched *only *though the nucleosynthetic products of PopIII stars (Fig.5). *The expected number of 2G stars is negligible in the observed sample, independent on the Z**cr** value.* In Beers & Christlieb [12] sample (2876 stars) only 1-2 stars could retain the metal-free nucleosynthetic imprint.

- Fig.6: Impact of 2G stars for the fiducial model and Zcr =10–4 ,10– 6, 0. The highest histograms show the total MDF while the smaller represent the MDFs for  2G stars. The percentage show the 2G fraction with respect to the total in the range in which they appear.

**References**

- astro-ph/0611130

**Z****cr ****= 10****–****4 ****Z******** **

**Z****cr ****= 10****–****4 ****Z******** **