Exam/Project? •black holes & galaxy evolution •star formation history of the Universe •galaxy formation •DLAs & link to galaxies •the First stars •simulating galaxies 1 Resolving Galaxies Tolstoy, Hill & Tosi 2009, ARAA, 47, 371 2 The Field of Streams Belokurov et al. 2006, ApJL, 642, 137 3 Distribution of small systems CVn II Com CVn I Boo IIIKoposov 1 Willman 1 Boo I Leo II UMa I Boo II Leo V Segue 1 Leo I Leo T Ursa Minor Leo IV UMa II Sextans Draco Her Koposov 2 o l=180 l=0o, b=0o l=-180o Sagittarius Segue 3 Carina LMC Segue 2 Pisces II SMC Fornax Sculptor Courtesy Vasily Belokurov 4 Boötes I D ~ 60kpc MV ~ -5.8 Rh ~ 220pc previous value new Giraffe value FLAMES/Giraffe velocities are both precise and reliable è taking dSph kinematics to the Koposov et al. 2011, ApJ, 736, 146 most extreme ultra-faints. Belokurov et al. 2006, ApJL, 647, 111 5 A Word of Caution: “Evolution” of Boötes I 9.0±2.2 km/s or Munoz et al, 2006 Metallicity 6.6±2.3 km/s Norris et al, 2010 Dispersion 4.6±0.8 km/s or Martin et al, 2007 Velocity 2.4±0.9Koposov etkm/s al, 2011 dispersion Norris et al, 2010 Stellar Metallicity Belokurov et al, 2006 Okamoto et al, 2011 Size 2006 2011 We are still learning how to study these objects! Vasily Belokurov ● Institute of Astronomy, Cambridge 6 The Effect on Global Properties... Common Mass Scale 2006 2011 Boötes I Strigari et al, 2008 Vasily Belokurov ● Institute of Astronomy, Cambridge 7 Segue 1 Segue 1 Sgr leading tail Sgr trailing tail Niederste-Ostholt et al, 2009 Vasily Belokurov ● Institute of Astronomy, Cambridge 8 HST CMDs of Ultra-faints Brown et al. 2012 ApJL 9 Lecture Nine: Galaxy Formation ...fluctuations to galaxies… Longair, chapter 11 - 13, 16 Monday 11th March 10 Galaxy Formation Why is the universe populated by galaxies, rather than a uniform sea of stars? Why are most stars in galaxies with luminosities near L ~ 3×1010 L (Schechter fn) ? ⋆ ⊙ Longair, p. 77 What is the physical origin of the fundamental plane of elliptical galaxies? Longair, p. 71 and the Tully–Fisher law for disk galaxies? Longair, p. 73 These are the kinds of questions that a complete theory of galaxy formation should answer. 11 ç ? δρ/ρ ~ 10-5 δρ/ρ ~ 106 (galaxies), 1000 (clusters) 12 Cosmic History Big Bang time present 13 Growth of Perturbations density ρ and pressure p velocity distribution is v the gravitational potential Φ at any point is given by: Conservation of mass eqn of continuity Longair, p. 313-17 Euler’s eqn eqn of motion of fluid element Poisson’s eqn Gravitational potential Lagrangian coords Co-moving coordinates, x = a(t)r, where r is co-moving coordinate distance and a(t) is the scale factor, so that δx = δ[a(t)r] = rδa(t) + a(t) δr. Perturb these equations by a very small amount Eliminate the peculiar velocities by taking the co-moving divergence of Euler‘s equation and the time derivative of the continuity equation, combining these & remembering Poisson’s eqn, get a wave equation adiabatic perturbations are related via the sound speed to pressure and density and given Δ = δρ/ρ Seek wave solutions for Δ, where kc is the wave-vector in co-moving coords Wave equation for Δ 14 The Jeans Instability Wave equation for Δ Longair, p. 317-18 Jeans criterion: we have an oscillating solution where the pressure gradient is sufficient to support the region if the right hand side is positive. If it is negative we have an exponentially growing (or decaying) solution and the gravitational attraction is stronger than the pressure. dispersion relation unstable modes In terms of wavelength: Jeans instability timescale Physical basis is very simple – the instability is driven by the self-gravity of the region and the tendency to collapse is resisted by internal pressure gradient. It is also possible to derive Jeans instability criterion by considering the pressure support of a region, pressure p; density ρ; and radius r. dp/dr ~ -p/r 3 2 M ~ ρ r and since cs ~ p/ρ region becomes unstable if hydrostatic support Jeans Length Thus the Jeans Length is the scale which is just stable against gravitational collapse Note: the Jeans length is the distance a sound wave travels in a collapse time 4 M = ⇡⇢R3 3 ρ Δ=δρ/ρ rJ 15 The Jeans Instability Virial Theorem: 2K + U = 0 Describes the condition of equilibrium for a stable, gravitationally bound system gravitational potential energy of a spherical cloud of constant density cloud’s internal kinetic energy, no. of particles, 4 M = ⇡⇢R3 3 initial mass condition for collapse density of cloud Jeans Mass write in terms of sound waves, p=Aργ from ideal gas law (γ=5/3) Jeans Mass 16 Evolution of Jeans Mass Longair, p. 319-20; p. 350-55 Bender, IMPRS Astrophysics Introductory Course 17 Evolution of Jeans Mass The temperature dependence of the Jeans mass changed dramatically Longair, p. 350-55 at the time of recombination T for radiation & matter equal RADIATION DOMINATED UNIVERSE MATTER includes dominant DOMINATED effect of photons UNIVERSE 18 Longair, p. 355-57 19 Oscillations & Damping The temperature dependence of the Jeans mass changed dramatically at the time of recombination Longair, p. 355-57 an adiabatic fluctuation smaller than this would not Effect of dark matter survive past recombination. 2970K; µ = 0.584 (for X=0.77; Y=0.23) SILK DAMPING Rate of growth of density perturbations 20 Theory vs. Observation Temperature fluctuation maps of the CMB from WMAP give ΔT/T ~ 10-5 at z~1000, as the earliest evidence for inhomogeneities. CMB fluctuations can at best (in a critical density universe) grow by a factor 1/(1+z) = R ~ 1000 by today, and thus we should expect for the amplitude of baryon fluctuations today: In sharp contrast to the large Therefore, in a purely baryonic universe we cannot inhomogenieties observed in understand how galaxies and clusters could form! the local universe! DARK MATTER DRIVES GALAXY EVOLUTION Coles & Lucchin 1995 21 Dark Matter & Baryons Coupled Perturbations: Evolution of perturbations that contain distinct components (e.g., baryons & dark matter) Time dependence of two different modes means that baryons can fall into dark potential wells and quickly match the dark matter perturbations. This means that Universes containing dark matter can produce small anisotropies in the microwave background: radiation drag allows dark matter to undergo growth between matter-radiation equality and recombination, while the baryons cannot. Baryons follow Dark Matter 22 Two collapse scenarios: Initial collapse Hierarchical merging (top down) (bottom up) ρ ρ θ θ Fragmentation ρ ρ θ θ ρ ρ Merging θ θ which scenario - depends on nature of dark matter 23 Bender, IMPRS Astrophysics Introductory Course 24 Cold dark matter • Devised to explain rotation curves and missing mass in clusters. • Assumed non-interacting except via gravity. • Also required to explain large-scale structure and CMB. • Numerical simulations on cosmological scales • Power law of initial fluctuations set at CMB surface. • Growth via gravity alone. • Robust prediction of Large Scale Structure. • Halo build-up via hierarchical merging. • Testable under assumption light traces matter • Numerical simulations can now predict dark matter distributions very well (20 million particles+gravity) 25 Standard ΛCDM model After two its principle constituents, vacuum energy and cold dark matter • On large scales the Universe is homogeneous & isotropic (Friedman- Robertson-Walker metric) • Geometry of Universe is flat, as predicted by inflation -2 • Present densities of baryonic matter, Ωb0 = (0.0455 ±0.0015)h7 , dark matter, Ωm0 = (0.237 ±0.034) and vacuum energy ΩΛ0 = 1 - Ωm0 = 0.763 ± 0.034, where h7 = 1.05 ± 0.05. • Dark matter is cold (random velocity at decoupling ~50km/s) • Initial density fluctuations in density were small (|δ|<<1) and described by a random gaussian field. • Initial power spectrum of density fluctuations was approximately a Harrison- Zeldovich spectrum, P(k) ∝ kn, where n=1 26 post-recombination era z~1000 0 z~1000 reionisation (z~6-7): the dark ages.... reionisation occurred 30 > z > 6 0 < z < 6-7 observable Universe of galaxies intrinsically non-linear nature of processes involved makes the subject an ideal challenge for large scale computer simulations which can give clues to underlying astrophysics. following the gas too complex semi-analytic models... 27 Biased Galaxy Formation: Peaks and Patches Galaxies form at peaks in the density field. Threshold decreases with time leading to more and bigger galaxies. 28 Non-linear collapse of density perturbations Longair p. 471-2 The density of a luminous galaxy at a radius of a few kpc is ~105 times larger than 11 -2 -3 critical density, ρc (=1.3599x10 h7 M¤Mpc ). Thus, galaxy formation involves highly non-linear density fluctuations, and our linear formulism must be supplemented by approximate analytic arguments and numerical simulations to follow structure formation into the non-linear regime. Although full development of gravitational instability cannot be solved exactly without N-body techniques there are some very useful special cases and approximations that help to understand the general case, 29 Spherical (Top-Hat) Collapse Longair p. 472-4 A calculation that can be carried out exactly is the collapse of a uniform spherical density perturbation in an otherwise uniform Universe The dynamics of such regions are precisely the same as those of a closed universe with Ω0 > 1 The variation of the `scale factor’, or relative size, of the perturbation ap is cycloidal and given by the parametric solution to the Friedman model (matter dominated Universe) The perturbation reached maximum size at `turnaround’, when it stopped expanding, at = 0 at θ=π and so has separated out of the expanding background.