1. IAC, La Laguna, 31/01/2008 SEMI-ANALYTIC MODEL OF GALAXY FORMATION Elena Ricciardelli Padova University In collaboration with Prof. Alberto Franceschini G alaxy E volution C O de

2. IAC, La Laguna, 31/01/2008 OUTLINE AND MOTIVATION Galaxy Evolution is a two stages process: dark haloes forming in a dissipationless, gravitational collapse, while galaxies inside them follow the radiative cooling of barions SAM model: coupling two kind of approches for the full description of the growth of structure Monte Carlo realizations for the forest of merger trees: advantages and drawbacks Analytic recipes involving barions: cooling, SF, feedback, galaxy interactions Comparison with local observations High-redshift universe: how galaxies formed and assembled their mass

3. IAC, La Laguna, 31/01/2008 PRESS-SCHECHTER APPROACH Press & Schecter (1974): Number of haloes collapsing at redshift z with mass within M and M+ΔM per unit of volume are computed assuming that overdensities greater than δ c collapse to form virialized haloes Barrier: time variable ~(1+z) per SCDM Variance of the density field: mass variable ~M -α

4. IAC, La Laguna, 31/01/2008 EXTENDED PRESS-SCHECHTER APPROACH Lacey and Cole, 1993: Given an halo with mass M 1 at t 1, we need the number density of haloes with mass M 2 at t 2 (t2>t1) Conditional mass function: Given the probability of finding a progenitor of mass M, we can split a parent halo in arbitrary subclumps for a given redshift Subclump of the parent halo: younger and less massive More massive halo

5. IAC, La Laguna, 31/01/2008 ELLIPSOIDAL COLLAPSE Ellipsoidal collapse the shape of the barrier depends on mass PS mass function does not match perfectly the MF from N-body simulations: overabundance of small objects and underpredictions of massive ones Spherical collapse barrier=δc(t) better agreement with ellipsoidal collapse (Sheth & Tormen 2002)

6. IAC, La Laguna, 31/01/2008 Consider mass M 0 at redshift z=0 compute probability P that it has a progenitor of mass M 2 at redshift z 2 draw a mass from the probability and compute the remaining mass M 0 -M 2 iterate the procedure on the progenitors masses found at the next timestep until all the progenitors fall below the mass resolution Mass resolution arbitrary, chosen M(Vc=40 km/s)  ~10 10 M ๏ at z=0 MTREE: Tracking the Merging History

7. IAC, La Laguna, 31/01/2008 MTREE: Sheth & Lemnson method Sheth & Lemson(1999): Partition algorithm for WN spectrum (P(k)~k 0 ) extendend to ΛCDM spectrum M0M0 f(M 1,δ c1 | M 0,δ c0 ) From EPS or ST ditributions M1M1 R=M 0 -M 1 M2M2 f(M 2,δ c1 | R,δ cR ) It gives an exact distribution of progenitors masses for WN case, in order to obtain ΛCDM masses we consider each chosen M wn as populated by ν progenitors with mass M LCDM  obtained assuming volume conservation

8. IAC, La Laguna, 31/01/2008 Spherical collpase (EPS): perfect agreement with theoretical predictions at all redshifts and parent masses Ellipsoidal collapse (ST): good agreement except lowest redshift time-steps, low progenitor masses EPS ST M halo =1 x 10 11 M ๏ M halo =1 x 10 13 M ๏ MTREE: Conditional Mass Functions

9. IAC, La Laguna, 31/01/2008  Grid in time: 52 time-step between z=49 and z=0  Grid in halo masses: 35 parent halo from M=10 10 M ๏ up to 10 15 M ๏  Number of progenitor haloes at zcut are normalized with PS or ST number density at z=0 Perfect agreement with theoretical expectations in both cases: even EC collapse model at low masses works very well: masses that lead to discrepancies in the CMF at low- z live only in high-mass haloes, very rare, small contribution to total MF MTREE: Unconditional Mass Functions

10. IAC, La Laguna, 31/01/2008 MTREE: Mass Accretion History M main vs z M all vs z sum of the mass of all the progenitors above the minimum mass Formation redshift for the main progenitor greater for less massive systems Formation redshift for the sum of all the progenitors is greater for more massive systems

11. IAC, La Laguna, 31/01/2008 GECO: Galaxy Evolution COde  We start at the bottom of the hierarchy assigning a barionic mass for each halo: M hot =f B M DM  Hot gas at the virial temperature of the halo: T vir ~V c 2  During halo mergers, galaxies inside them keep their identity, due their higher concentrations z We end up at z=o with a lot of sub- units for each haloes

12. IAC, La Laguna, 31/01/2008 GECO : Gas Cooling I Sutherland & Dopita cooling function Gas is shock-heated to T vir, the pressure of the gas supports it against further collapse Gas can subseguently cool via radiative processes and accretes to the center of the halo  Rate at which gas cools: t cool =thermal energy content/cooling rate The radius at which the cooling time is equal to the age of the universe, assuming an isothermal distribution, is r cool Accretion rate determined by t cool and t ff

13. IAC, La Laguna, 31/01/2008 GECO : Gas Cooling II COLD MODE  r cool > R vir for low mass, high z object Gas cools very rapidly and the cooling rate is equal to the rate at which diffuse gas is added to the halo HOT MODE  r cool < R vir for high mass, low z object RvRv

14. IAC, La Laguna, 31/01/2008 GECO: Star Formation QUIESCENT MODE: BURST MODE: during galaxy merger cold gas is converted in stars at a much higher rate f=m1/m2 t burst =t dyn Up to 100% (major merger) of gas is converted in star in 10-50 Myrs SF efficiency, free parameter disk bulge

15. IAC, La Laguna, 31/01/2008 A certain fraction of stars is in massive, fast evolving stars that become SNII SN inject gas and energy in the ISM, reheting cold gas: GECO: SN Feedback More effective for low mass haloes, weak potential wells, not able to retain gas SN efficiency, free parameter gas becomes again available for cooling

16. IAC, La Laguna, 31/01/2008 QSO MODE: during galaxy mergers the gas mass accreted is proportional to the total cold gas mass with an efficiency dependent on the ratio of the masses of the merging galaxies GECO: AGN Feedback Seed BH mass in each “top-halo”:1000 M๏, they grow through BH-BH mergers and through the accretion of gas in 2 ways: RADIO MODE: continuos and quiescent accretion on to a central SMBH, order of magnitude below Eddinghton limit Heating generated by BH accretion: This injection of energy compensates the cooling rate

17. IAC, La Laguna, 31/01/2008 GECO: Galaxy Interactions SATELLITE-CENTRAL  dynamical friction timescale t DF ~M halo /M sat SATELLITE-SATELLITE  random collisions σ ~ v gal /V vir When a new halo forms the most massive galaxy becomes the central galaxy, the only one that can accrete the gas of the halo and all the other ones are satellites Merger  STARBURST Major merger(m1/m2>0.3)  disks are destroyed, stars added to the bulge component

18. IAC, La Laguna, 31/01/2008 GECO: Stellar Population Synthesis Bursty SF (C+C & S+S) Major Merger DISK BULGE Given the SED of a population of stars formed at the same time and with the same metallicity L λ (t,Z) we convolve it with the SFH of the galaxy to obtain the galaxy SED: SSPs from Bressan 1994 dust extinction dependent on age: E(B-V) decreasing with age Quiescent SF L B /L D gives the morphology index

19. IAC, La Laguna, 31/01/2008 GECO: Setting free parameters α SF  star formation efficiency ε SN  efficiency in reheting gas from SN f B H  efficiency of the BH accretion in radio mode (all life) k QSO  efficiency of the BH accretion in QSO mode (mergers) Constraints:  TF relation  Local SMF  BH-Bulge relation Local observations

20. IAC, La Laguna, 31/01/2008 GECO: Local Stellar Mass Function Good match at intermediate-massive galaxies, excess of faint galaxies, shaped by SN feedback and satellite collisions  different source of feedback needed? Dominated by disks at low masses and by bulges at high masses ε SN f BH, k QSO α SF Local MF (Cole et al., 2001) GECO predictions

21. IAC, La Laguna, 31/01/2008 GECO: BH-BULGE relation Haring & Rix, 2004 From a sample of 30 nearby galaxies Very good match of the zero-point and the slope of the relation Growth of BH closely linked to SB and bulge growth log(M BH ) log(M bulge )

22. IAC, La Laguna, 31/01/2008 GECO: Evolution of the MF The model predicts a strong evolution of the bright-end of the MF between z=1 and present time

23. IAC, La Laguna, 31/01/2008 GECO: Evolution of the MF Comparison with observations: MF from Franceschini et al. (2006) High mass galaxies already in place at z=1, while we predict a much higher evolution

24. IAC, La Laguna, 31/01/2008 GECO: Quiescent vs Bursty SF Quite eterogeneous SFHs: Sp: protracted up to recent times; raising at high-z and then declining at low-z E: truncated SF after a burst (merger), combined effect of gas consumed & AGN Good correlation between age/color/morphology M halo =5 x 10 12 M ๏ (MW) Formation redshift: z at which half of the present stellar mass is FORMED z=2 z=1 z=0

25. IAC, La Laguna, 31/01/2008 GECO: Central vs Satellites CENTRAL M halo =5 x 10 12 M ๏ (MW) Only central galaxies accretes cold gas from the halo reservoir, satellites stop to accrete gas at the time they enter in a halo bigger than their host  Time of accretion rowghly equal to the time of SF truncation

26. IAC, La Laguna, 31/01/2008 GECO: SFH vs Environment M halo =3 x 10 11 M ๏ Low-mass haloes: galaxies with continuos SF, mainly in a quiescent way (z=0.5-1) High-mass haloes: galaxies with more bursty SF, E morphology, redder colors and high redshift of formation (z~2) M halo =3 x 10 13 M ๏

27. IAC, La Laguna, 31/01/2008 GECO: SFH vs Environment M halo =3 x 10 11 M ๏ M halo =3 x 10 13 M ๏ Averaged SFH over 10 realizations of the same halo

28. IAC, La Laguna, 31/01/2008 GECO: z FORM vs M halo High-mass haloes contain older galaxies, that formed half of present-day mass at high-z In agreement with the down-sizing behaviour of observed galaxies

29. IAC, La Laguna, 31/01/2008 GECO: SF vs Mass Assembly M halo =3 x 10 11 M ๏ M halo =3 x 10 13 M ๏ Smooth assembly of mass over time: it exactly reflects the stellar mass formed in each time-step  almost all of the present mass is formed in the main progenitor MAJOR MERGER Mass assembled during 3 episodes of major merger, which destroy the disk, assembly time very different from formation time, half of the present mass is assembled between z=1 and z=0

30. IAC, La Laguna, 31/01/2008 GECO: to be improved High-mass galaxies, which live in high-mass haloes, are formed recentely in the model in comparison with observations Extended tail of SF in the central galaxies of high mass haloes Late assembly epoch for these objects: half of their mass assembled below z=1 Dry merger too frequent?How to stop them?

31. IAC, La Laguna, 31/01/2008 CONCLUSIONS MC merger tree for the growth of DM haloes, for EPS and ST distributions, good agreement with theoretical expectations GECO code tested on local observations, global good match of the local SMF, but excess of low-mass objects Local BH-Bulge masse perfectly reproduced Bright-end of the SMF evolves too much in comparison with the one observed SFHs: galaxies show different histories of SFH depending on the mass of the halo where they live, galaxies in high mass haloes on averege form half of their mass at z=2 with a tail of SF at lower z Assembly histories: in several cases the assembly history is very different from SFH, galaxies in high-mass haloes assemble the bulk of their mass after z=1  this leads to a great evolution in SMF

32. IAC, La Laguna, 31/01/2008 GECO: Future plans  Apply SAM code to EC mtree and mtree from N-body simulations  Confirm results with improved statistics  Introduce chemical evolution  Better treatment of dust: improve the modelling of extinction and introduce the riemission of dust at long wavelenghts  comparison with FIR data

33. IAC, La Laguna, 31/01/2008