MltiMulti-wavel th d lli flength modelling of galaxy ...staff.on.br/etelles/lectures/lacey-2.pdf ·...

M lti l th d lli fMulti-wavelength modelling of galaxy evolution:galaxy evolution:

Lecture 2: Semi-analytical ymodels of galaxy formation

Cedric LaceyCedric Lacey

10/04/2006 Foz de Iguacu 1

Outline

• Why multi-wavelength modelling of galaxy l ti ?evolution?

• Basics of semi-analytical galaxy formation models

• A tale of 2 models - does the IMF vary?y• Chemical evolution in hierarchical models -

further evidence for a variable IMF?further evidence for a variable IMF?


Why multi-Why multiwavelengthwavelength

d lli ?modelling?


Why do we need multi-wavelength y gmodels of galaxy evolution?

(i.e models which cover wavelengths from UV to IR or radio)

1. Different wavelengths provide

IR or radio)

g pcomplementary information

- sensitive to different physical processes2. Multi-wavelength view of galaxy evolution

now becoming observationally accessible- GALEX satellite in far-UV, SPITZER in IR, SCUBA-2

in sub-mm, VLA in radio….


2 different views of the2 different views of the Hubble Deep Field

optical sub-mm

Universe looks very different at different wavelengths!10/04/2006 Foz de Iguacu 5

Universe looks very different at different wavelengths!

Key Motivation: Understand StarKey Motivation: Understand Star Formation History of universe

• Cosmic SFR history describes how baryons converted into stars over history of universe - fundamental yquantity in models of galaxy formation

• Many attempts to determine SFR• Many attempts to determine SFR history observationally - but different methods each have own limitations, and final answer still uncertain


Methods to measure SFRMethods to measure SFRFor distant galaxies cannot observe individualFor distant galaxies, cannot observe individual stars, so must infer SFR from some property of integrated light:

1. Far-UV continuum from stars (912 < integrated light:

λ < 3000A)2. IR or sub-mm continuum from dust (10 (

µm < λ < 1 mm)3 Emission lines from HII regions3. Emission lines from HII regions4. Radio continuum (usually non-thermal)

(λ > 10 cm)10/04/2006 Foz de Iguacu 7

(λ > 10 cm)

1 SFR f f UV ti1. SFR from far-UV continuum• In galaxies with significant star formation, non-

ionizing far-UV (FUV) continuum dominated by O & B stars with lifetimes < 100 MyrB stars with lifetimes < 100 Myr

• So if could measure L(FUV) without dust extinction, could infer formation rate of stars with m > 5 Mo

• However, in most galaxies, dust extinction in FUV very large

&• Furthermore, no reliable & accurate way to measure this dust extinction from FUV continuum alone (various empirical methods, but do not work for all(various empirical methods, but do not work for all types of galaxies)


2. SFR from IR & sub-mm continuum

• Most star formation appears to happen in dusty regions with τ(UV) > 1g ( )⇒ most UV luminosity from young stars absorbed by

dust grains & then re-radiated in IR & sub-mm⇒ total IR luminosity (integrated over 10 < λ < 1000

µm) should provide good measure of formation rate of m > 5 Mo stars in most casesrate of m > 5 Mo stars in most cases

• However, measurement of L(total IR) only currently possible for local galaxies


• For high-z galaxies, can only measure L in mid-IR or sub-mm, then convert to L(total IR) based on assumed SED shapeassumed SED shape

• But SED shapes in IR/sub-mm vary, so this is uncertain (mid-IR & sub-mm both miss peak of dust ( pemission in far-IR, λ ∼ 100 µm)


3 SFR from HII region3. SFR from HII region emission linesemission lines

• HII region emission lines (e.g. Lyα, Hα, [OII]) produced by gas ionized by O & B stars (lifetimes <produced by gas ionized by O & B stars (lifetimes < 10 Myr)

• If could measure unextincted luminosities of H-recombination lines (e.g. Hα) would give direct measure of rate of H-ionization, hence formation rate of stars with m > 10 Moof stars with m > 10 Mo

• Can try to estimate dust extinction observationally from recomination-line ratios (e.g. Hα / Hβ) - but only works for simple dust geometries, and v.difficult at high-z


4. SFR from radio continuum

• Low-frequency radio continuum in star-forming galaxies dominated by synchrotron emissiongalaxies dominated by synchrotron emission

• Synchrotron emission thought to be powered by Type II supernova explosionsII supernova explosions

• So L(radio) should provide measure of SNII rate, hence formation rate of stars with m > 8 Mohence formation rate of stars with m 8 Mo

• Advantage: L(radio) not affected by dust• Disadvantage: conversion L(radio)/rate(SNII) mightDisadvantage: conversion L(radio)/rate(SNII) might

depend on magnetic fields


Measuring SFRs: the IMFMeasuring SFRs: the IMF uncertaintyuncertainty

• All methods (1) - (4) only measure formation t f i t ( 5 10 M )rate of massive stars (m > 5-10 Mo)

• To get total SFR, have to extrapolate down to low masses (m = 0.1 Mo) based on an assumed IMF

• What if the IMF varies with environment? - e g if it is different in normal & starburste.g. if it is different in normal & starburst

galaxies ?


Measuring cosmic SFR:Measuring cosmic SFR: the LF uncertaintythe LF uncertainty

• Want to obtain total SFR/(comoving volume) as function of redshift zfunction of redshift z

• This requires summing SFRs of ALL galaxies in representative volume of universerepresentative volume of universe

• In practice, at high-z only observe highest luminosity galaxiesgalaxies

• Have to extrapolate contribution of low-L galaxies based on assumed luminosity function (LF)y ( )

• But LF shape varies with wavelength & redshift, so this introduces further uncertainties


Example of observational data on pcosmic SFR history

• variety of methods shown: far-UV, Hα, s b mmsub-mm

• with/without i f dcorrections for dust

extinction


How to test cosmic SFR history ypredicted by a galaxy formation

model against observations?model against observations?• Since current obsns only probe some rangesSince current obsns only probe some ranges

of wavelength & luminosity• also given uncertainties from dust extinction &also given uncertainties from dust extinction &

IMF=> most robust way to compare models with> most robust way to compare models with obsns is to compare predicted & observed LFs at wavelengths actually observedg y

• Multi-wavelength modelling allows one to do this


Semi-analyticalSemi-analytical models of galaxymodels of galaxy

formation


Galaxy formation in the CDMGalaxy formation in the CDM model: key physical processesmodel: key physical processes• Assembly of dark matter halosAssembly of dark matter halos• Shock-heating and radiative cooling of

gas within halos• Star formation and feedbackStar formation and feedback• Production of heavy elements• Galaxy mergers


Semi-analytical models

• Start from initial density fluctuations• Use analytical and/or Monte Carlo

modelling for the different physicalmodelling for the different physical processesP di t l ti ( di• Predict galaxy properties (mass, radius, luminosity, metallicity etc) and their evolution with redshift


Some references on semi analyticalSome references on semi-analytical models

• White & Rees (1978)• White & Frenk (1991) Lacey et al (1991)• White & Frenk (1991), Lacey et al (1991)• Kauffmann, White & Guiderdoni (1993), Cole et al

(1994)( )• Somerville & Primack (1999)• Cole et al (2000), Granato et al (2000)( ) ( )• Guiderdoni et al (2001), Nagashima et al (2001),

Menci et al (2002)B h l (200 )• Baugh et al (2005)

• and many more……


CDM concordance modelCDM concordance model• CMB anisotropies

30≈Ω

• CMB anisotropies

• Galaxy clustering

//707.0

3.0

≈≈Ω

≈Ω

MpcskmHvac

CDM• H0 from HST key project

• acceleration of universe from

1)(

04.0//700

∝

≈Ω≈

nkkPprimordial

MpcskmH

nb

acceleration of universe from high-z supernovae

• big-bang nucleosynthesis9.0

1,)(

8 ≈≈∝

σlinearnkkPprimordialbig-bang nucleosynthesis

• baryon fraction in galaxy clustersclusters

• number density of galaxy l t

10/04/2006 Foz de Iguacu 21clusters

Assembly of dark matterAssembly of dark matter halos: Merger treeshalos: Merger trees

• Assembly history of halo described by merger tree

• 2 approaches:• Monte Carlo based on• Monte Carlo based on

conditional Press-Schechter mass function

• Extract from N-body simulations

• similar results from bothsimilar results from both approaches


Shock heating & cooling ofShock-heating & cooling of gas in halosgas in halos

• Infalling gas all shock-heated to halo virial temperature

• Radiative cooling of gas from static sphericalfrom static spherical distribution

• Disk size related to angular momentum of gas which cools


Shock heating & cooling ofShock-heating & cooling of gas: more detailsgas: more details

• Assume halo gas shock-heated to uniform temperature:temperature:

Tvir = µmHVc2 / 2k

• Assume halo density profile:ρ (r)∝1/ r2ρH (r)∝1/ r

or

ρH (r)∝1/ r(r2 + rs2 )


• Assume gas density follows dark matter orAssume gas density follows dark matter, or modified profile with core, e.g.

( ) 1/( 2 + 2 )ρgas (r)∝1/(r 2 + rc2 )

• Radiative cooling time in halo then depends g pon radius through:

t l (r) = 3kT i / 2n (r)L(T i ,Z )tcool (r) 3kTvir / 2ngas (r)L(Tvir ,Zgas )where L(T,Z) is radiative cooling function for

lli i l i i ti lib icollisional ionization equlibrium• At time t after halo has formed, gas cools out

to radius rcool(t) given by:tcool (rcool ) = t


cool cool

Disk radius• if it conserves its angular momentum, cooled

gas collapses to form rotationally-supported gas co apses to o otat o a y suppo teddisk with radius roughly:

r ~ λ rrdisk ~ λHrcoolwhere λ is halo spin parameter

• more detailed calcn of disk radius depends on halo profile and disk self-gravity


Star formation & feedback

t f i di k• stars form in disks

*/τgasMSFR =• supernova feedback ejects gas from galaxies

g

SFRVM j )(β=&


SFRVM ceject )(β

Star formation timescale in disks

• A popular choice is:τ* = α τ dyn

where τdyn is dynamical time in diskdyn

• Another popular choice:τ cV α*τ* = cVc

• or some combination of these…


Supernova feedback

• Usually assume SN feedback efficiency of form

β = (V /Vh )−αhotβ = (Vc /Vhot )where αhot & Vhot are parameters

αhot =2 corresponds to constant efficiency of converting SNII explosionefficiency of converting SNII explosion energy into gas ejection energy


Galaxy mergers & morphology

• halos merge

• galaxies merge by dynamical frictiony

• major mergers make galactic spheroids fromgalactic spheroids from disks

• mergers trigger• mergers trigger starbursts

spheroids can grow new• spheroids can grow new disks


Effects of galaxy mergersEffects of galaxy mergers• Galaxy mergers with mass ratio M2/M1 > 0.3 cause

major changes in galaxy morphologies

- trigger re-arrangement of stellar disks into spheroids- these are MAJOR MERGERs

• Smaller mass ratios produce minor morphological changes

th MINOR MERGERS- these are MINOR MERGERS• Major mergers trigger STARBURSTS which consume

remaining gasremaining gas• Minor mergers may also trigger bursts (but with lower

efficiency)10/04/2006 Foz de Iguacu 31

y)

Modelling galaxy SEDsModelling galaxy SEDs

use GRASIL model to compute emissionto compute emission from stars, extinction and emission by dust, and radio emission

(Silva et al 1998)


• semi-analytical model tracks evolution of ymetallicity of stars & gas

assume dust/gas proportional to gas metallicity• assume dust/gas proportional to gas metallicity

• optical depth for dust depends on both dust mass p p pand galaxy radius


Example Model SED (1)Example Model SED (1)

• unextincted starlightunextincted starlight

(+ radio)



• starlight with duststarlight with dust extinction




• emission from• emission from diffuse dust




• emission from• emission from diffuse dust + molecular clouds




• emission from• emission from diffuse dust + molecular clouds

• total


T d l fTwo models of galaxy formationg y

both based on same ΛCDM cosmology- both based on same ΛCDM cosmology


Model 1Model 1(Cole et al 2000, Granato et al 2000)

• Star formation timescale in disks:V ατ* = cτ dynVc

α*

- scaling with τdyn implies much shorter diskscaling with τdyn implies much shorter disk SFR timescales at high-z

• Starbursts triggered by major mergers onlyStarbursts triggered by major mergers only• Normal solar neighbourhood IMF for all star

formationformation


Model 2Model 2(Baugh et al 2005)

• Star formation timescale in disks:ατ* = cVcα*

- longer disk SFR timescales at high-z c.f.longer disk SFR timescales at high z c.f. Model 1 => high-z disks more gas-rich

• Starbursts triggered by major & minorStarbursts triggered by major & minor mergers

=> Starbursts make much larger contribution to=> Starbursts make much larger contribution to total SFR at high-z


Model 2 (cont’d)Model 2 (cont d)

• Normal solar neighbourhood IMF for stars formed quiescently in galaactic disksformed quiescently in galaactic disks

• Top-heavy (x=0) IMF for stars formed in b t t i d b lbursts triggered by galaxy mergers

=> Starbursts much more luminous because of larger fraction of high-mass stars


Choice of free parameters

• For both Models 1 & 2, adjust free parameters to fit wide range of observational data on present-day p ygalaxies:

luminosity functions in optical near IR- luminosity functions in optical, near-IR, far-IR; disk sizes & circular velocities; gas fractions, metallicities, mix of morphological types etc


p g yp

Star formation history bothStar formation history both modelsmodels

model 1 model 2

quiescent quiescent

i t

bursts bursts

quiescent

burstsbursts

model 2 has more star formation in bursts at high z10/04/2006 Foz de Iguacu 44

model 2 has more star formation in bursts at high z

Present-day optical & near-IR y pluminosity functions (Model 1)

B-band K bandB band K-band


Present-day far-IR LF (Model 1)Present-day far-IR LF (Model 1)60 µm

quiescent

burstsbursts


Present-day optical & near-IR y pLFs (Model 2)

B-band K-band

total t t lquiescent

quiescentno dust

no dust

total total

burstsbursts

bursts

Very similar to Model 1 - this is because free parameters in model chosen to try to match present day galaxies


model chosen to try to match present-day galaxies

Present day luminosity LFs in far-IR & radio (Model 2)

far IR (60 m) radio (1 4 GHz)far-IR (60 µm) radio (1.4 GHz)

t t ltotal

quiescent

bursts

A i t h diff b t M d l 1 & 210/04/2006 Foz de Iguacu 48Again, not much difference between Models 1 & 2

• So both models predict very similar properties for local universe

• At high redshift however predictionsAt high redshift however, predictions differ dramatically….


Sub-mm (850 µm) source counts ( µ )(Model 1 vs Model 2)

t t l

Model 1 Model 2

burststotal

quiescent


Interpretation of sub-mm counts

• Sub-mm source counts appear to be dominated by ultra-luminous dusty starbursts at z~2

• the 2 models make very different predictions for the number of thesepredictions for the number of these

• what are the main reasons for the difference?


• allowing minor mergers to trigger bursts makes important a o g o e ge s to t gge bu sts a es po ta tcontribn, as does change in disk SFR timescale

• but main effect is from change in IMF in bursts10/04/2006 Foz de Iguacu 52

but main effect is from change in IMF in bursts

Galaxy luminosity function in y yrest-frame UV (1500A) at z=3

Model 1 Model 2

bursts

No dust extinction

total

quiescent With dustextinction


Interpretation of far-UV LF

• Comparison with observed far-UV LF at high redshift also favours model with top-heavy IMF in burstsp y

• But far-UV LF also more sensitive to details of dust model (especiallydetails of dust model (especially timescale for young stars to escape from parent gas clouds)


Ch i lChemical evolution


Chemical Enrichment: Supporting pp gevidence for top-heavy IMF?

• Calculate chemical enrichment including both SNII & SNIabot S & S a

• yields of different elements depend on IMF


Abundances in intracluster gasAbundances in intracluster gas

• model with solar neighbourhood IMF

top–heavy IMF

neighbourhood IMF predicts ICM abundances too low by f t 2 3

normal IMF

factor 2-3

• but top-heavy IMF in bursts gives givesbursts gives gives good match to obs

N hi t l 200510/04/2006 Foz de Iguacu 57X-ray temperature

Nagashima etal 2005

Stellar abundances in ellipticalsStellar abundances in ellipticals

• [α/H] vs σt h b

top-heavy IMF normal IMF top-heavy IMF

matches obs slightly better with top-heavy IMF

• [Fe/H] matches obsmatches obs for L* ellips

• but predictedbut predicted trend of [α/Fe] vs σ is wrong

10/04/2006 Foz de Iguacu 58Nagashima etal 2005

C l di kConcluding remarks…• Galaxy formation is very complicated, and

many uncertainties remain– especially concerning star formation & feedback

processes• So important to use as many different

observational constraints on models as possible

• And keep an open mind about possibility ofAnd keep an open mind about possibility of new physical effects, such as IMF variations


MltiMulti-wavel th d lli flength modelling of galaxy ...staff.on.br/etelles/lectures/lacey-2.pdf ·...

Documents

Transcript of MltiMulti-wavel th d lli flength modelling of galaxy ...staff.on.br/etelles/lectures/lacey-2.pdf ·...