Post-Recombination Era I. Between epoch of recombination & reionisation ( z ~ 1000 - 7) also known as the DARK AGES Exactly when reionisation took place is a key issue for contemporary cosmology Lecture Eight: II. The Observable Universe (z ~ 7 - 0) Populations of galaxies and quasars have been observed to evolve dramatically over this period. Galaxy Formation! ...from models to reality…! Bringing together the wealth of observational data into a convincing and coherent picture of galaxy formation and evolution is an important modern goal. The intrinsically non-linear nature of the processes involved makes the subject an Longair, chapter 16, 19 ideal challenge for large scale computer simulations - which can be used to try to plus literature understand the underlying physical processes. Thursday 4th March Dark and visible matter! Two collapse scenarios:! NGC 4216 Initial collapse Hierarchical merging (top down) (bottom up) ! ! " " Fragmentation ! ! " " ! ! Merging " " Signs of Galaxy formation thick disk open clusters thin disk thick disk bulge halo thick disk globulars young halo globulars old halo globulars Freeman & Bland-Hawthorn 2002 ARAA #CDM! Tegmark Spergel 2003, 2007 Collisionless Collapse! How is mass distributed?! Given that we see numerous signs of the presence of dark matter the calculations for a collisionless collapse are part of the standard picture for galaxy formation. (hot) White & Rees (1978) were the first to suggest that the formation process must be in two stages – baryons condense within the potential wells defined by the galaxies intracluster medium (ICM) dark matter collisionless collapse of dark matter haloes. This simplifies the problem in many way – since the complex fluid-mechanical and radiative behaviour of the gas can be initially ignored. Bottom-up, CDM small-scale perturbations survive recombination; consistent with heirarchical look of the universe (many galaxy groups and clusters). It may seem obvious that an infinitely nonlinear density field cannot be analysed within the bounds of linear theory – but a way forward was identified by Press & Schecter (1974). Their critical assumption is that even if the field is nonlinear the amplitude of large wavelength modes in the final field will be close to that predicted from linear theory. Mass function of collapsed halos! Press-Schechter Mass Function Analytic estimate of the mass function F(M), of bound objects in the Universe, defined such that F(M)dM is the co-moving number density of objects between M and M+dM. Objective was to provide an analytic formalism for the process of structure formation once the density perturbations had reached an amplitude that they could be considered to have formed bound objects. In good agreement with subsequent more detailed analyses and N-body simulations Assumption that primordial density perturbations were Gaussian fluctuations. Thus, the phases of the waves which made up the density distribution were random and the probability distribution of the amplitudes of the perturbations could be described by Gaussian function: large R is the density contrast associated with perturbations of mass M. medium R Being a gaussian distribution, the mean value is zero, with a finite variance $2(M) small R fraction of volumes This is exact statistical description of the perturbations 0 1.69 % implicit in the analysis of early universe. these spheres collapse The halo mass function Press-Schechter Mass Function the halo mass function is the number density of collapsed, bound, virialised structures assumption is that when the perturbations have developed an amplitude greater per unit mass, as a function of mass and red-shift than some critical value %c, they evolved rapidly into bound objects with mass M. The problem is thus completely defined, assume perturbations had power law spectrum P(k) = kn and we To illustrate how mass function changes with cosmic epoch need to chose value of spectral index (e.g., know the rules that describe the growth of the perturbations with cosmic epoch. Press & Schechter Harrison-Zeldovich spectrum) in the limit of small masses, critical Einstein-deSitter model assumed that the background world model was critical Einstein-deSitter model (&0=1 &#=0) so that the 2/3 perturbations developed as %' a' t right up to present epoch. #CDM straight forward extension. ((x) is the probabilty The mean square density perturbations on mass scale M are defined integral, defined by as being related to the power spectrum in this form: A, constant Can now express tc in terms of mass distribution Z=30 20 10 5 0 Here we introduce a reference mass: Press-Schechter Mass Function Since the amplitude of the perturbation %(M) grew as %(M) 'a ' t2/3 it follows that Press-Schechter halo mass function ! thus, A ' t4/3 and! The fraction of perturbations with masses in the range M to M+dM is: value at present epoch In the linear regime, the mass of the perturbation is Once the perturbation became non-linear, collapse mean density of begins and the result is a bound object of mass M, background model The space density N(M)dM of these masses is 1/V: F decreasing fn of increasing M Combining with: given that Mass distribution and how it evolved with time power law exponential This formalism only gives half the mass density being condensed into bound objects - because only the positive density fluctuations of a symmetric gaussian develop into bound systems. Because analysis small R medium R large R based upon the linear theory of perturbation growth. Press & Schechter were well aware of this issue, and suggested that their mass spectrum should be multiplied by a factor 2 to take account of accretion during non-linear stage. GADGET vs. Press-Schecter Millennium Simulation Large number density of low mass objects, 0 < z < 10 1.5%7%35%today Dark matter although derived for &0 =1; &# = 0 results are similar for #CDM Useful tool for studying development of galaxies and clusters of galaxies in hierarchical scenario. Springel et al. (2005) Springel et al. 2005, Nature, 435, 629 DARK MATTER DENSITY! Inner slopes! The halo profiles for different masses and cosmologies have the same “universal” functional form: r~r-1 and r~r-3 at small/large radii Scaled density profile of the most massive and least massive halos look very similar except at the core. The less massive halo has higher density at the center possibly due to the fact that they form earlier, and density perturbation at earlier times of the universe is more concentrated. Navarro, Frenk and White 1996 ApJ, 462, 563 concentration parameter, c ~ rvirial/rscale Navarro, Frenk and White 1997 ApJ, 490, 493 Photometry HSB and LSB galaxies! LSB galaxies: DM dominated?! Dynamics HSB galaxy LSB galaxies -2 HSB µB(0) = 21.65 mag arcsec Freeman's LAW (1970) -2 LSB µB(0) > 23 mag arcsec Verheijen & Tully 2003 Begeman 1989 Cusp problem! The inner Innerpotential of shape LSB galaxies of seem the to have potential slopes closer to! ) = 0 than ) = 1. de Blok & Bosma 2002 Spekkens, Giovanelli & Haynes 2005 de Blok & Bosma 2002 Luminosity Functions: Simulations vs. Observations Light can be a biased tracer of mass Reionisation and SN feedback ? AGN heating ? 12 10 M! Mass distribution of galactic halos from the observed luminosity function e.g., Sommerville & Primack 1999, MNRAS The mass function of dark matter halos is not in simple agreement with the observations. Current (long-standing) issues with (#)CDM How to encorporate baryons!? Numerical simulations predict dark matter distribution and it is presumed that the baryons are dragged along. However simulating baryons AND Only component we can easily and accurately measure. dark matter AND encoding baryon physics is complex and there is still much to work on here. ``gastro-physics’’ has been invoked to explain the differences between the observed (baryonic luminosity function) and the sub-halo mass function derived from N-body experiments. Three key problems with CDM model: At the low mass end, baryons must either be ejected from sub-halos or something must prevent them from collapsing 1.! Over production of low mass dark matter haloes along with the collapse of dark matter... 2.! Inner rotation curves much too steep, i.e., dense dark matter cores and something else must cause a steepening at the high 3.! Short stumpy (HSB) disks, i.e., no fragile thin disks (LSBs) formed. mass end. The role of dissipation Cooling catastrophe Dark matter particles are collisionless and only detectable in bulk by their gravitational influence Baryons, however, radiate - sure sign that dissipative Prescription for cooling straightforward, but the cooling times in the centres of processes are at work. massive halos extremely short (T ~ m2/3), and this would lead to very massive, Dissipative means - baryonic matter can loose energy by any number of radiative processes, resulting in a luminous central galaxies which are NOT observed loss of thermal energy from the system and so the baryonic component shrinks within in the dark matter halos. Once the gas within a system is stabilised by thermal pressure, loss of energy by radiation is an effective way of decreasing internal pressure, allowing region to contract and re-establish pressure equilibrium. If the radiation process is very effective in decreasing thermal energy and hence the pressure support of the system - runaway - thermal instability - cooling flow. Gas cools, settles into 2d disk, surrounded by 3d dark matter halo The role of dissipation Time scales Rees & Ostriker (1977) were first to consider this