galaxy formation and evolution with kband …：與k波段的星系的形成和演化…

1、 Formazione ed evoluzione delle galassie Scuola Normale Superiore Gennaio Febbraio 2006 Andrea Cimatti INAF Osservatorio Astrofisico di Arcetri (Firenze)Lecture 1 - OutlineVery general introduction to fundamentals of galaxy formationCosmological frameworkGrowth of perturbations ReionizationFirst obj

2、ects and Population III starsHierarchical merging models of galaxy formation The cosmological frameworkFriedmann-Lemaitre-Robertson-Walker modelFriedmann equationH = expansion ratea(t) = cosmic scale factor = 1+ztot = mass density Rcurv = curvature radius, Rcurv,0= (1/H0)/(0-1)1/2k = 0 (negative, fl

3、at, positive curvature)0 = tot/crit = tot/(3H02/8G)wX = characterizes the pressure of dark energy = pX/X10 parameters describe expansion, geometry, age and composition of the UniverseDeceleration parameterAge of the UniverseDensity parameter and geometrya(t)Geometry1 : sphericalThe era of “precision

4、” cosmologyFrom Freedman & Turner 2003Cosmological parameter from SNeSNe appear fainter than expected for either an open (M expansion timescaleEquivalence: z10000, end of the radiation era, begin of matter erawhen radiation density is equivalent to matter densityRecombination and decoupling: gradual

5、 process z1000-1500, electrons and protons start tocombine to form hydrogen atoms. Radiation moves independently of matter (no scattering)The Universe become transparent (CMB)At zz(dec) the first cosmic structures start to formPerturbationsThe idea is to understand what happens if a fluid is perturb

6、ed = 0 + / 1+z(eq), z(eq) = redshift at which (radiation)=(matter)(2) Evolution in a Universe with a fluid with equation of state p=wc2 with w=constCollisionless fluid (w=0) (e.g. dark matter particles), ultrarelativistic fluid (photons)(w=1/3), stiff matter (w=1)(3) Evolution with relativistic pert

7、urbations (radiative, rotational, scalar) (e.g. inflation)In general, it is always possible to find growing solutions for (t) when (Jeans)Non-baryonic Dark MatterHot Dark Matter: collisionless particles which are relativistic when matterand radiation decouple Cold Dark Matter: particles non-relativi

8、stic at the decouplingIn case of HDM, M(J,rec) 1014-15 Msun (e.g. neutrinos with mass 30 eV)In case of CDM, M(J,rec) “Top-down” scenario, fragmentation of “pancakes”Inconsistent with: galaxy clustering, peculiar motions, CMB fluctuationsCDM: the first perturbations which lead to gravitational collap

9、se have smallmasses = “Bottom-up” scenario, hierarchical clustering and merginglog(/)log R(t)/R0(t) -5 -4 -3 -2 -1 0 0-2-4-6(CDM)(baryons)(photons)Schematic evolution of /decouplingradiation eraMass Msun/ 10.0011e5 1e10 1e15Sub-galactic Galaxies ClustersHDMCDMDifferent forms of the fluctuation spect

10、rum at recombinationGrowth of perturbations summaryEPOCH (radiation) (CDM) (baryons)tt(enter)t(eq) grows as a2 grows as a2 grows as a2t(enter)tt(eq) oscillates grows as ln(a) oscillatest(eq)tt(dec) oscillates grows as a oscillatest(dec)t oscillates grows as a grows as at(enter) = epoch when a region

11、 with a scale length (or a mass contained in that region)enter the Hubble radius R=1/H(t), i.e. the scale over which physical processes operatecoherently and there is physical causality (cosmological horizon).Power spectrum and dark matterThe current power spectrum can be derived from the clustering

12、 at different scalesFreedman &Turner 2003Simulations of large scale sctructureVIRGO Consortium (1998)H0=50, =0.3, =0H0=50, =1, =0CDMCDM (H0=50, (m)=1, ()=0)Simulations of large scale sctructure at z=0479 MpcMass variance2(M) = (M-)2 / 2 = 1/2(M) = rms mass fluctuations= mean amplitude of matterdistr

13、ibution fluctuations within R(M) grows with time as 1/(1+z) (up to z1)(at z1 dark energy starts to dominate)Miralda-Escud 2003Bound objects form when primordial fluctuationsreach an amplitude 1Mean mass within R: =(4/3)R3 = VMass variance within V :Fluctuations and collapse1-5-Each object that forms

14、has a velocity dispersion(v) determined by its massand the size of the regionfrom which it collapsed:v2 GM/Rand a corresponding virialtemperature of the gas:kT(vir) = (mH) v2(=mean particle mass in unitsof the hydrogen mass)T(vir) determines the physicsof the rate at ahich gas cancool to form stars

15、Curves indicating which halos collapse from (1,2,3,4,5)- fluctuations of 1/2 (e.g. a 106 Msun halo can collapse at z20 from 3 fluctuation, or a Milky Way object can collapse at z1 from 1 or at z5 from 3 fluct.)Baryon cooling (1) A cloud with mass M and radius R is supported against gravitational col

16、lapse by gas pressure if it is at the virial temperature (i.e. stable) T(vir)GM/5RThe primodial gas (H + He plasma) can cool (= reduce pressure) via :1) bremsstrahlung (free-free emission due to acceleration of a chargedparticle in the Coulomb field of another charge; e.g. free electrons) 2) recombi

17、nation (an electron is captured by an ion into a bound state witha consequent emission of a photon; e.g. Hydrogen Balmer line emission)3) Compton scattering (energy transfer from hot electrons to colder cosmicbackground photons, important only at very high redshifts) The evolution of a gas cloud dep

18、ends on the cooling vs. dynamical timescale:t(cool) 3kT/2 (T) t(dyn) (/2)(2GM/R3)-1/2 =mean molecular weight of the gas 0.6m(H) for completely ionized gas, Y=0.25, Z=0For T104 K and no Compton scattering:(T) = cooling function = A(B)T1/2 + A(R)T-1/22 A(B), A(R) = terms due to free-free and recombina

19、tionBaryon cooling (2)t(cool) Hubble time never collapseHubble time t(cool) t(dyn) can collapse only on cosmological timescalet(cool) t(dyn) rapid cooling, loss of pressure support and free-fall collapseIn case of Dark Matter + baryons: t(cool) depends only on baryon density t(dyn) depends now on to

20、tal (=DM+baryon) densityWhat is the origin of the 1011 Msun mass-scale in the galaxy mass function ?It is thought that the condition t(cool)t(dyn) is what determines the galaxy mass scaleThe cooling diagramT (K)Mass (Msun) Velocity (km/s)1e91e81e71e61e51e41e9 1e10 1e11 1e12 1e13 1e14 1e1510300Irregu

21、larsSpiralsEllipticalsClusterst(cool)=t(dyn)t(cool) t(dyn) (no collapse)R=1 kpcR=1 MpcDark Ages and Pop III stars“Dark Ages”, reionization and first starsLoeb & Barkana 2001“Dark Ages”, reionization and first starsWMAP results indicate z(reionization) 10-20Quasars at z6 place a limit and indicate th

22、at at z6 there are some observations suggestingthat the fraction of atomic hydrogen increases rapidly (Gunn-Peterson trough)Miralda-Escud 2003Loeb & Barkana (2001)Gunn-Peterson effectQSOObserverGunn-Peterson:atomic H isdominant completesuppression offlux shortwardof Ly-Lyman- forest:flux partiallyab

23、sorbed by atomic H clouds,but n(H)z1. This probability is used to build the merging histories, alsocalled “merger trees” (e.g. Lacey & Cole 1993; Kauffmann & White 1993).Assumption: DM halos have angular momentumAssumption: DM halos have a density profile (e.g. NFW)Assumption: the mean rotational ve

24、locity of concentric shells of DM is constant with radius and always aligned in the same directionIt is believed that angular momentum and rotation originates from “tidal torques”and it is assumed all the material within the DM halos have this angular momentumThe typical fraction of baryons to dark

25、matter within a halo is(baryons)/(DM) 0.045/0.23 as derived for example by the WMAP resultsMerging trees Baugh et al 98Example ofhierarchicalmerging fromthe SAM+N-bodysimulations of theGALICS model(Hatton et al. 2004)Step 2 Baryons, gas, coolingDiffuse gas is heated by shocks during halo collapse an

26、d merging eventsThis gas component is usually called “hot” and it is assumed that it is heated to the virial temperature of the halo (hydrostatic equilibrium):kT=(mp/2)Vc2 T 36 (Vc/km/sec)2 K (mp= gas mean molecular weight) A fraction of this gas can cool and the cooling at each radius is linked tot

27、he choice of the gas density profile (equal to or different from DM profile)The cooled (“cold”) gas looses its pressure support and naturally settles into a diskStep 2a Disk formationWhen the gas cools is not supported anymore by pressure/temperature (i.e. random motions of the particles) against gr

28、avitational collapseHowever, if there is an initial angular momentum, the rotational velocityincreases during the collapse (angular momentum conservation)When the rotational velocity is equal to the DM halo circular velocity,the system reaches the equilibrium supported by the centrifugal force DISKS

29、tep 3 “Quiescent” star formationThe cold gas can be converted into stars through a star formation process thatcan be written as:dM*/dt = M(cold)/t* Msun/yrThe key issue is what to adopt as t* ! t* = constant same star formation efficiency any time and anywhere t* = t*(0)(Vc/V0) powerlaw of circular

30、velocity (e.g. = -1.5), independent of z t* = t*(0)r(disk)/Vc proportional to dynamical time of the galaxy = f(z)Step 4 FeedbackStar formation affects the physical state of the surrounding gas asstellar winds and Supernovae inject energy and re-heat (thermal feedback)and/or eject (kinetic feedback)

31、gas from disk and/or haloThe star formation also enriches of metals the ISM (chemical feedback) Gas metal enrichment decreases the cooling time allowing more gas to cool laterstar metal enrichment affects colors and luminosities of the stellar populationsdM(re-heat)/dt (Vvir / V0)-(f) dM*/dt, with (

32、f) typically = 2M(re-heated) is then either added to M(hot) (retention) or ejected from halo (rejection)Some recent models include also the feedback from AGN Granato et al. 2004Step 5 Chemical evolutionIt is usually adopted a scenario where:a fraction R of the newly formed stellar mass M* is returne

33、d immediately back to ISM RM*and produces a mass YM* of newly synthesized metalsThe remaining (1-R)M* is assumed to live in stars foreverR and Y depend on Initial Mass Function (IMF)R and Y are rather uncertain : R 0.3-0.4 , Y 0.01-0.03Feedback and chemical enrichmentCole et al. 2000Step 6 Mergers a

34、nd spheroid formation It is assumed that when DM halos merge, the most massive galaxy automatically becomes the central galaxy in the new halo, while all theother galaxies become “satellites” orbiting within the DM haloThe orbits of satellite galaxies gradually decay due to the loss of energyand ang

35、ular momentum through dynamical friction to the halo materialand they spiral in and merge with the central galaxy Some models include also merging between satellitesThe galaxy morphology depends on the mass (stars+cold gas) ratio of the mergers: M2/M1 f(ell) “major” merger stars form ellipsoid, cold

36、 gas undergoes starburst M2/M1f(ell) “minor” merger0.3 f(ell) 1.0Spheroids/bulges can form also from unstable disks bar spheroidStep 7 Stellar populations and dustStarting from the star formation rate and metallicity given by SAMsIt is possible to use the stellar population synthesis models and ISMM

37、odels to compute the fluxes and spectra at any time and wavelengthThis step assumed a constant and universal stellar initial mass function (IMF)The treatment of dust must include absorption, scattering and emission Step 8 Normalization of SAMs to observablesTwo main observables are used for the normalizationThe local galaxy luminosity functions (typically in B and K bands)The properties of our Galaxy (Tully-Fisher normalization, cold mass fraction)Some problems of CDM and SAMsAre the density profiles predicted for DM halos (e.g. Navarro-Frenk-