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 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 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 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

The role of dissipation Time scales Rees & Ostriker (1977) were first to consider this issue in the formation of large Compare cooling timescale with gravitational collapse timescale: scale baryonic structures. Silk & Wyse (1993) included more complex cooling depending on the level of enrichment. The key relation is the energy loss rate of the plasma by radiation as a function of temperature. Not only initial fluctuation spectrum - also dissipative processes

Cooling due to thermal bremsstrahlung and Compton scattering Cooling dominates

Perturbations such low density, no collapse on hubble time Dynamical processes determine behaviour of baryons

Cooling time shorter than 6 12 ionisation/recombination T H He gravitational collapse time, so Critical locus: 10 ! M/M! ! 10 dissipative processes are more important than dynamical processes in Silk & Wyse (1993) Phys. Rep. 231, 293 determining the behaviour of Silk & Wyse (1993) Phys. Rep. 231, 293 baryonic matter. Why are there no galaxies with M>1013M ? sun Cosmological cooling diagram So far we have been mostly concerned with dark matter halos. The distribution 9 15 DM halos in mass is continuous from ~10 to ~10 Msun. But, DM halos with 12 M>few x 10 Msun are not observed to host galaxies, only clusters of galaxies. Why?

Z=0, photoionisation about 1/10 of virial &=0.3

radius, r200 for both Cooling curve diagram &=1 galaxies

Z=0 gas has cooled gas has not cooled clusters

Whether a galaxy forms in a given halo is determined by the rate of gas cooling. Z= solar

It is dissipation which determines whether a collapsed object is described as a galaxy or a system of galaxies.

adapted from Blumenthal et al. (1984), by Peacock (1999)

Large Scale Structure of the Universe How to treat poorly understood

Somewhat after recombination -- processes? density perturbations are small on nearly all spatial scales. •! Gas cooling Dark Ages, prior to z=10 -- •! Star formation density perturbations in dark matter and baryons grow; on smaller scales perturbations have gone non-linear, *>>1; •! Feedback small (low mass) dark matter halos form; massive stars form in their potential wells and reionize the Universe. within #CDM hierarchical merger scenario z=3 -- Most galaxies have formed; they are bright with stars; this is also the epoch of highest quasar activity; •! Cosmological parameters known to ~10% galaxy clusters are forming. Growth of structure on large (linear) scales has nearly stopped, but smaller non-linear •! Large populations of galaxies detected at all red-shifts up to z~5 scales continue to evolve. •! Readily available large computing power z=0 -- Small galaxies continue to get merged to form larger ones; large scale (>10-100Mpc) potential wells/hill are decaying.

Picture credit: A. Kravtsov, http://cosmicweb.uchicago.edu/filaments.html Basic Facts Cooling Stars form only from cool gas. For the last 25 years work on galaxy formation has been dominated by the belief that when a density perturbation goes non-linear and collapses, baryons are shock

Feedback from star formation creates hot gas: heated to the virial temperature,Tvir, so the raw material for galaxy formation is hot •!easily ejected from low-mass systems gas, and galaxies form by the cooling of virial temperature gas (Rees & Ostriker 1977; White & Rees 1978). So galaxy formation is regulated by the rate at which •!in high-mass systems it is retained and does not cool. gas is able to cool in the dark matter haloes.

This model has been developed further by many people especially to include the We have very well determined luminosity functions, spectral energy distribution effect of mergers and the evolution of the stellar population (e.g., White & Frenk 91; and star formation histories for large samples of galaxies at a range of redshifts Cole 1991; Kauffmann, White, & Guiderdoni 1993; Lacey et al. 1993; Cole et al. to constrain how these competing and fundamentally linked process proceed. 1994, 2000; Kauffmann et al. 1999; Somerville & Primack 1999; Benson et al. 2002) We also have the Local Group whose formation process we can study in great detail and must be compatible with global determinations. All these models lead to strong cooling in the centre of large systems (cooling catastrophe) and an over density of smaller systems - various attempts have been made to overcome this by invoking various additional physics, such as feedback, ionisation, merging etc.

The detailed and accurate luminosity functions from SDSS extensive and accurate surveys are now actively challenging these models.

How does gas fall into potential well? Semi-analytic models of galaxy formation & evolution Understanding the underlying physical processes in baryons is not yet at a level where it can be accurately built into large scale hydro-dynamical simulations. The gas initially has the same spatial distribution as the dark matter Include empirical rules for star formation, supernovae rates, element enrichment etc into the large scale hydro-dynamical simulations. As fluctuations in the dark matter separate from the Hubble expansion, turn around and collapse, the gas is assumed to Main free parameters: be heated by shocks as it falls into the gravitational potential •!Star formation: changes have weak effect on L, but strong effect on correlation between gas fraction well of the dark halo, producing a hot gas halo that is and mass supported against further collapse by the pressure of the gas •!Return fraction: changes have effect on metallicity •!Feedback efficiency: increase feedback " decrease L, with bigger effect at small mass Rees & Ostriker 1977 MNRAS, 179, 541; •!Efficiency (per solar mass of gas to stars) of metal production: more metals " more cooling in small White & Rees 1978 MNRAS, 183, 341 mass halos " more L at small mass •!Timescale for reincorporating ejected gas: if long then this is effectively like feedback The gas attains the virial temperature of the •!Normalize: to match Luminosity Fn (Durham) or to match Milky Way (Munich) halo, which depends upon the mass of the halo First attempts came in 1991 by three groups, which eventually merged into two Dark matter haloes are supported against further groups [Durham (Frenk) & Munich (White)]: gravitational collapse by a pressure created by the thermalized velocities of the dark matter particles. White & Frenk 91 (updating White & Rees); Cole 91 ; Lacey & Silk 91 Expect hot halos that should radiate in X-rays, but are not detected, e.g., Benson et al. (2000) First attempts to put the processes into dark matter haloes: Baugh 2006 Reports on Progress in Physics, 69, 3101 Kauffmann, White & Guiderdoni 1993; Cole et al. 1994 Star formation &

dark matter It all starts with a merger tree...!

Kauffmann et al. 1999

merger history determines ! The merging history of DM halos galaxy morphology! Given the fraction of matter at redshift z in collapsed halos with mass M, one can calculate the fraction of matter which is in halos of mass M1, at redshift z1, and later in halos of mass M0, at redshift z0: f(M1,M0,z1,z0).

One can then obtain the conditional probability that material which is in halo

M0, at z0, had previously been in halo M1, at redshift z1. Bower, 1991, MNRAS 248,332 f (M1,M0 ,z1,z0 ) f (M1,z1 | M0 ,z0 ) = fraction of matter in halos M and z f (M0 ,z0 ) 0 0

The number of (M1, z1) progenitors M0 N(M1,z1) = f (M1,z1 | M0 ,z0 ) of a single (M0, z0) halo is: M1 construct a “tree” that determines how a single dark matter halo will break up into a set of progenitors at some earlier red-shift. One cannot simple select halo progenitors randomly 1.0E14 according to the given probability distribution because the mass of a halo must be equal to the Kauffmann & White, 1.0E12 sum of masses of progenitor halos at every stage. 1993, MNRAS 261, 921

Merger trees can be used to calculate the evolution and morphological Explaining the Luminosity Fn transformation of galaxies, taking into account gas and star formation. Reionisation and redshift SN feedback ? z = 0 z = 100 Press Schechter

Halo of mass M0 at z=0

AGN heating ?

12 10 M!

Mass distribution of galactic calculate time to merge using halos from the observed dynamical friction estimate luminosity function

Benson et al. 2003 ApJ, 599, 38

Explaining the Luminosity Fn photoionisation Only Photoionization suppresses the formation of small galaxies (sometimes Cooling called “Squelching”, Somerville 2002), so that surviving satellites are preferentially those that formed before the Universe reionized. As a result, the number of satellites expected today is about an order of magnitude smaller than the number inferred by identifying satellites with subhaloes of the same circular velocity in high-resolution simulations of the dark matter.

“overcooling”

Benson et al. (2002) MNRAS, 333, 177 Somerville (2002) ApJL, 572, 23 Benson et al. 2003 ApJ, 599, 38 Explaining the Luminosity Fn ! Feedback Star formation rate is affected when cold gas is reheated by the energy ejected by supernovae explosions and stellar winds, thus moving gas from star forming regions (e.g., disk) into a diffuse halo. The SN energy fed to the gas in haloes compared to the energy required for significantly heating the gas, gives a maximum halo virial velocity for which SN

feedback is important Vc ~ 100km/s. Only in haloes smaller than this can SN feedback significantly suppress subsequent star formation

Formation of dwarfs surpressed after Universe is reionised

Benson et al. 2003 ApJ, 599, 38

Star formation rate is affected when cold gas is reheated by the energy ejected by supernovae explosions and stellar winds, thus moving gas from star Star-Formation forming regions (e.g., disk) into a diffuse halo. 49 ESN ~ 10 ergs per we hide all our M! star formed for ignorance in +* a standard IMF

sometimes related to

size (Vc) of halo rvir

Heating caused by star-formation

stars form and metals are produced; cold gas (and metals) heated and ejected from the galaxy either retained in the halo rturnaround Dekel & Silk 1986 or ejected entirely ejected gas returns to the halo when larger scale collapses e.g., Somerville & Primack 1999; Benson et al. 2003 Mac Low & Ferrara 1999 Mac Low & Ferrara 1999

8 z=10; 10 M! Mac Low & Ferrara 1999 ApJ, 513, 142 Mori et al. 2002 ApJ, 571, 40

Disk reheating Adding SN feedback

Schaye et al. 2000 ApJL, 541, 1 Benson et al. 2003 ApJ, 599, 38

Balancing radiative cooling Conduction Expelling gas from dark Expulsion with thermal conduction matter halo

Have to assume an extremely high Total energy requires significantly conduction efficiency exceeds that available from SN alone.

Benson et al. 2003 ApJ, 599, 38 Benson et al. 2003 ApJ, 599, 38