Lecture fifteen:

Friday 21st March

ΛCDM Universe (contd)

Longair chap. 13, 16

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ONLY predicts dark matter distributionNGC 4216

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dissipation

how goes gas collapse in a dark matter halo?

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The role of dissipation

Dark matter particles are collisionless and only detectable in bulk by their gravitational influence Baryons, however, radiate - sure sign that dissipative processes are at work.

Dissipative means - baryonic matter can loose energy by any number of radiative processes, resulting in a 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

Longair p. 477-82

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Physical properties

Dark matter halo with total mass M that virialize at redshift z and has a gas mass content Mg = Ωb/Ωm M

where :

Barkana&Loeb2001 5

What sets the mass of the first galaxies?

This is a necessary but not a sufficient condition for the collapse.

We need to cool down the gas very rapidly

The Jeans mass after recombination

Mass of First galaxies

Barkana & Leob 2001 Physics Reports, 349, 1256

Fundamental timescales

Cooling : Free-fall :

Hubble :

tc > tH no cooling tH >tc > tff quasi-static cooling tc < tff rapid cooling ! free fall collapse

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The cooling function

Barkana&Loeb2001

H2

H

nH = 0.045 cm-3

nH2 = 0.1% nH

Primordial composition gas bremsstrahlung

Lya-cooling Roto-vibrational transition

H2-cooling mini-haloes

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Molecular hydrogen formation

main formation channel:

main destruction channel:

The presence of electrons is crucial in order to produce H2 After recombination ye ≈ 3 ×10-4 from which we get fH2 ≈ 2×10-6

This is too low to allow the collapse

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The first galaxies are expected to be associated with H2-cooling minihaloes,

that have total masses M ∼ 106M� virial temperatures Tvir ~ 2000K,

and that assembled at redshift z ∼ 25–30. These objects correspond to 3σ density fluctuations

of the density field.

The mass of the first galaxies

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Reionization

time

redshift

Isolated HII regions

Overlapping stage

At zrei the reionization is complete

zrei ≈ 6 from QSOs absorption spectra

zrei ≈ 11 from CMB Thompson optical depth

Courtesy of A. Maselli

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Chemical feedback

The presence of metals and dust drives the transition from a �primordial� star formation mode (massive stars) to the �normal� star formation mode observed in the local Universe.

!  Z < 10-4 Z! !  m* > 10 M! !  IMF?

!  Z = [10–4–1] Z! !  m*=[0.1-100]M! !  IMF : Salpeter

Local observations

Z ≤ Zcr Z > Zcr

Theoretical studies

PopIII stars PopII/I stars

Zcr=10 –5±1Z!

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Mechanical feedback

The energy deposition associated with the first SN explosions may induce partial or total gas removal from the galaxy itself

The ejection efficiency depends on the halo binding energy (Eb) and on the kinetic energy released during the explosion (Ekin)

Eb = GM2/2rvir ≈ 2.3×1053 erg (M/108M!)5/3[(1 + z)/10] Esn = εw NSN <ESN >

The star formation is reduced in low mass objects The IGM out of which haloes form is gradually metal enriched

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Mechanical feedback M = 108M!

@ z ≈ 9

multiple SN explosions

Mori, Madau, Ferrara 2002

48 kpc 12 kpc 3 kpc

~ 5 Myr

~ 8 Myr

~ 20 Myr

~ 35 Myr

~ 175 Myr

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Mechanical feedback M = 1011M!

Stars log[ρ*cm3]

Gas log[ρgcm3]

Metals [O/H]

Mori&Umemura2006

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Implications

Radiative feedback influences the mass of the subsequent �generation of galaxies� by increasing the minimum halo mass able to form stars Chemical feedback influences the mass of the second generation stars by driving the transition from massive PopIII stars to normal PopII/I stars. Mechanical feedback influences both the mass of subsequent generation of galaxies and stars by removing the gas in low mass haloes and by enriching the IGM out of which more massive haloes virialize.

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Dark Matter & Baryons

Big Question:

Does gas that falls in immediately shock heat to the virial temperature; then galaxies form as this gas cools (Rees & Ostriker 1977; White & Rees 1978)

ORDoes a significant fraction of this infalling gas fail to heat up and galaxies are formed directly from this fraction (Binney 1977; Birnboim & Dekel 2003). The hot gas never cools & is “lost”. This heated fraction grows and makes galaxy formation less efficient

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Cooling

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

This model has been developed further by many people especially to include the effect of mergers and the evolution of the stellar population (e.g., White & Frenk 91; Cole 1991; Kauffmann, White, & Guiderdoni 1993; Lacey et al. 1993; Cole et al. 1994, 2000; Kauffmann et al. 1999; Somerville & Primack 1999; Benson et al. 2002)

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.

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 heated to the virial temperature,Tvir, so the raw material for galaxy formation is hot 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 gas is able to cool in the dark matter haloes.

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How does gas fall into potential well?

The gas initially has the same spatial distribution as the dark matter

Dark matter haloes are supported against further gravitational collapse by a pressure created by the thermalized velocities of the dark matter particles.

Baugh 2006 Reports on Progress in Physics, 69, 3101

As fluctuations in the dark matter separate from the Hubble expansion, turn around and collapse, the gas is assumed to be heated by shocks as it falls into the gravitational potential well of the dark halo, producing a hot gas halo that is supported against further collapse by the pressure of the gas

Rees & Ostriker 1977 MNRAS, 179, 541; White & Rees 1978 MNRAS, 183, 341

Expect hot halos that should radiate in X-rays, but are not detected, e.g., Benson et al. (2000)

The gas attains the virial temperature of the halo, which depends upon the mass of the halo

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dE

dT= �N2⇤(T )

The role of dissipationRees & Ostriker (1977) were first to consider this issue in the formation of large 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.

Silk & Wyse (1993) Phys. Rep. 231, 293

Fully ionised plasma

N, number density ofhydrogen ions.

energy loss rate

time it takes plasma to radiate away its themal energy

ener

gy lo

ss r

ate

temperatureionisation/recombination T H He

T> 106K - cooling dominated by thermal bremsstrahlung

free-bound & bound-bound transitions

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Time scalesCompare cooling timescale with gravitational collapse timescale:

Silk & Wyse (1993) Phys. Rep. 231, 293

Cooling time shorter than gravitational collapse time, so dissipative processes are more important than dynamical processes in determining the behaviour of baryonic matter.

Not only initial fluctuation spectrum - also dissipative processes

Dynamical processes determine behaviour of baryons

Perturbations such low density, no collapse on hubble time

Critical loci: 106 ≤ M/M! ≤ 1012

Radiation loss time = age of universe

num

ber

dens

ity

temperature

tcool

< tdyn

tcool

= tdyn

only works if cooling undisturbed, if merging then gas will be reheated and collapse may never occur.

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Cosmological cooling diagram

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

Z= solar

Z=0

Z=0, photoionisation

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

clusters

galaxies

ac

6

mass, assuming 10% baryonic

cooling=collapse time

virialised 3σ fluctuations

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Cooling catastrophe

Prescription for cooling straightforward, but the cooling times in the centres of massive halos extremely short, and this would lead to very massive, luminous central galaxies which are NOT observed

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Another option

When a proto-galaxy collapses, a fraction f of its gas fails to heat to the virial temperature, where f is large for low mass haloes.

Subsequently cold gas frequently falls into galactic haloes. In the absence of a dense atmosphere of virial temperature gas it builds up on nearly circular orbits and can be observed in the 21-cm line of H I. When there is a sufficiently dense hot atmosphere, cold infalling gas tends to be ablated and absorbed by the hot atmosphere before it can form stars.

Binney 1977 ApJ, 215, 483; Binney 2004 MNRAS, 347, 1093

Importance of cool gas:•Standard picture: gas heated to Tvir on falling into Φ (Rees & Ostriker 1977; White & Rees 1978)•Another proposal is that a fraction f enters at T<<Tvir (Binney 1977; Katz et al 2003; Birnboim & Dekel 2003)•f~1 on galaxy scales M* and below

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Gas temperature in a slice of proto-galaxy

Dekel & Birnboim 2006; Dekel et al. 2009

Two different epochs, two different masses

At z≃ 4, relatively massive halo, M≃ 3×1011M�.

Much of the gas is heated by a strong shock near the virial radius (white circle). Cold streams penetrate through the hot medium deep into the halo.

At z≃ 9, is small, M≃ 2×1010M�. The gas

flows in cold (T�Tv), showing no evidence for shock heating inside the virial radius (circle).

Massive halos at high red-shift can have cold streams and clumps embedded in the hot (spherical) medium.

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Critical shock-heating halo massRv , virial radius

Dekel & Birnboim 2006

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Cooling mechanisms

Dekel et al. (2009), Nature, supp. info

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Origin of bi-modalityz>2: continuous gas supply, regulated by SN feedback; galaxies evolve along the blue sequence, which extends beyond shock-heating mass due to cold streams in hot media

z<1: in the absence of cold streams above Mshock, the shock-heated gas is kept hot by AGN feedback, gas supply and star formation shut down, and the stellar population passively turns red and dead. Gas-poor mergers stretch the red sequence towards larger masses

blue sequence is dominated by galaxies in haloes below Mshock, as they grow by accretion/mergers. Cold flows lead to early disc growth and star formation, which is regulated by SN feedback over cosmological times. Galaxies can get very blue because of repeating starbursts due to the clumpy gas supply and the interplay between infall, starburst and outflow.

red sequence when a halo is more massive than Mshock, halo gas is shock heated; it becomes dilute and vulnerable to AGN feedback. At z < zcrit, where cold streams are suppressed, gas supply from the host halo shuts off, preventing any further growth of discs and star formation and the stellar population passively turns 'red and dead'

Dekel & Birnboim 2006

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Cooling mechanisms

Dekel & Birnboim 2006

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Cooling & Bimodality

Cattaneo et al. 2006, MNRAS 370, 165Dekel & Birnboim 2006

New ingredient: shut down in gas cooling and star formation above Mshock~ 1012M! after zcrit~3 while allowing for efficient star formation by cold streams before zcrit

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Fitting the luminosity fn.

Cattaneo et al. 2006

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Relative numbers red & blue

Cattaneo et al. 2006

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Disc formation in a cosmological context

This snapshot of a state-of-the-art simulation shows the flow of gas into a fledgling galaxy. Streams of cold gas (blue) flow onto the edge of the fledgling galaxy’s disk, while shock-heated gas (red) surrounds the disk. Gas enriched in metal content (green) by supernova explosions is stripped from smaller galaxies interacting with the hot dark matter halo and the cold gas stream.

Agertz et al. 2009 MNRAS, 397, L64

Mvir ~3.5x1011M!

Mbar~2.4x1010M!

(50% gas)Cold flows+shocks

33 34

Basic FactsStars form only from cool gas.

Feedback from star formation creates hot gas:

•easily ejected from low-mass systems

•in high-mass systems it is retained and may not cool.

We have very well determined luminosity functions, spectral energy distribution and star formation histories for large samples of galaxies at a range of redshifts to constrain how these competing and fundamentally linked process proceed.

We also have the Local Group whose formation process we can study in great detail and must be compatible with global determinations.

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Galaxy Evolution

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Gasoline, an N-body + smoothed particle hydrodynamics (SPH) code that allows for a large dynamic range due to its Lagrangian nature and includes the physics of star formation, heating by an UV background, SNe type Ia and type II feedback (blast-wave) and enrichment, and cooling. No black holes or AGN feedback are included in this run. Eris was run on the NASA Pleiades supercomputer consuming roughly 1.6 million cpu-hours (9 months including testing overhead) from z=90 to z=0.Here are some basic facts of Eris at z=0 (and a rough comparison to the MilkyWay):

Guedes et al. 2011 ApJ, 742, 76

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Guedes et al. 2011 ApJ, 742, 76

https://webhome.phys.ethz.ch/~jguedes/eris.html

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Guedes et al. 2011 ApJ, 742, 76

Comparison to Milky Way

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Guedes et al. 2011 ApJ, 742, 76

Comparison to Milky Way

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following the gas too complex semi-analytic models...

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Semi-analytic models of galaxy formation & evolution

Include empirical rules for star formation, supernovae rates, element enrichment etc into the large scale hydro-dynamical simulations.

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.

Main free parameters:•Star formation: changes have weak effect on L, but strong effect on correlation between gas fraction and mass•Return fraction: changes have effect on metallicity•Feedback efficiency: increase feedback → decrease L, with bigger effect at small mass•Efficiency (per solar mass of gas to stars) of metal production: more metals → more cooling in small mass halos → more L at small mass•Timescale for reincorporating ejected gas: if long then this is effectively like feedback•Normalize: to match Luminosity Fn (Durham) or to match Milky Way (Munich)

First attempts came in 1991 by three groups, which eventually merged into two groups [Durham (Frenk) & Munich (White)]:

White & Frenk 91 (updating White & Rees); Cole 91 ; Lacey & Silk 91

First attempts to put the processes into dark matter haloes:

Kauffmann, White & Guiderdoni 1993; Cole et al. 1994

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Kauffmann et al. 1999

Star formation & dark matter

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