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The physics of galaxy formation
LAGOS-URBINA, CLAUDIA,DEL,PILAR
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The physics of galaxy formation
ClaudiadelP.Lagos
Abstract
Weinvestigateimproved,morephysicalmethodsformodellingkeyprocessesingalaxyformation
that take place in the interstellar medium, and study their effects on the observed properties and
evolutionofgalaxies. Thetopicsweinvestigateare: (i)improvementstotherelationbetweenthe
star formation rates (SFRs) and the cold gas contents of galaxies; (ii) how to predict the atomic
and molecular gas masses in galaxies with different properties, (iii) how to predict the emission
of widely used molecular tracers, such as carbon monoxide (CO); and (iv) the gas outflows from
galaxiesdrivenbysupernovaeandtheirdependenceonlocalandglobalpropertiesofgalaxies. We
performthesestudiesusingthesemi-analyticmodelofgalaxyformationGALFORM,andfullyembed
ourcalculationsinacosmologicalscenario,theΛcolddarkmatterparadigm. Thisisdonewiththe
dualaimsofunderstandinghowthephysicalprocessesaboveaffectgalaxyformationandevolution
inastatisticalfashion,andtoimproveandextendthepredictivepowerofgalaxyformationmodels.
WefindthatbycalculatingtheSFRfromthemoleculargascontentandrelatingthemolecular-to-
atomic mass ratio in the interstellar medium to the hydrostatic pressure in the midplane of the
disk, we can explain the observed atomic gas mass function and clustering of galaxies selected
by their atomic hydrogen mass, the SFRs of local and high-redshift galaxies, the evolution of the
molecular hydrogen gas fraction and the global atomic hydrogen abundance of the universe, and
the local scaling relations between gas contents and other galaxy properties. We also find that
by coupling GALFORM with a radiative transfer and interstellar chemistry code describing photon
dominatedregions, ournewmodelcanexplaintheobservedemissionofCOfromdifferenttypes
of galaxy. Finally, based on a physical description of the dynamical evolution of bubbles created
by supernovae in the interstellar medium, we find that the outflow rate driven by supernovae
dependsstronglyonthesurfacedensityofgasplusstarsandthegasfraction. Wecriticallyrevise
the phenomenological prescriptions widely used to describe supernova feedback in the literature
andproposenewphysicallymotivatedprescriptions.

The physics of galaxy formation
by Claudia del P. Lagos
AthesissubmittedtoDurhamUniversity
inaccordancewiththeregulationsfor
admittancetotheDegreeofDoctorofPhilosophy.
DepartmentofPhysics
DurhamUniversity
September2012

Contents
1 Introduction 1
1.1 StarformationinthelocalanddistantUniverse . . . . . . . . . . . . 6
1.1.1 Atomicandmolecularhydrogeningalaxies . . . . . . . . . . 8
1.2 Observationsofoutflowsingalaxies . . . . . . . . . . . . . . . . . . . 11
1.3 Towardsaphysicalmodeloftheinterstellarmedium,starformation
andsupernovafeedback . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Thesisoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Thegalaxyformationmodel 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Formationandgrowthofdarkmatterstructures . . . . . . . . . . . . 19
2.2.1 Thehalomassfunction . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Halomergertrees . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Haloproperties . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Gascoolinginhalos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Starformation,chemicalenrichmentandsupernovafeedback . . . . 25
2.4.1 TheoriginalstarformationlawsinGALFORM . . . . . . . . . . 26
2.4.2 Theefficiencyofstellarfeedback . . . . . . . . . . . . . . . . . 27
2.4.3 Recycledfractionandyield . . . . . . . . . . . . . . . . . . . . 28
2.5 Othersourcesoffeedback . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.1 PhotoionisationheatingoftheIGM . . . . . . . . . . . . . . . 29
2.5.2 AGNfeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Galaxymergersanddiskinstabilities . . . . . . . . . . . . . . . . . . . 31
i
2.6.1 Galaxymergers . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.2 Diskinstabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.7 Galaxysizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.8 TheSpectralEnergyDistributionofgalaxies . . . . . . . . . . . . . . 34
2.8.1 Emissionoflight . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.8.2 Dustextinction . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.9 MaindifferencesbetweentheBau05andBow06models . . . . . . . . 36
3 On the impact of empirical and theoretical star formation laws on galaxy
formation 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Modellingthestarformationactivityingalaxies . . . . . . . . . . . . 43
3.2.1 Thegalaxyformationmodel . . . . . . . . . . . . . . . . . . . 43
3.2.2 RemarksontheoriginalstarformationlawsinGALFORM . . . 44
3.2.3 Thenewstarformationlaws . . . . . . . . . . . . . . . . . . . 44
3.3 TheevolutionoftheSFRdensity . . . . . . . . . . . . . . . . . . . . . 48
3.4 Coldgasmasscontentofgalaxies . . . . . . . . . . . . . . . . . . . . . 51
3.4.1 Coldgasmassfunction . . . . . . . . . . . . . . . . . . . . . . 51
3.4.2 Globalcoldgasdensityevolution . . . . . . . . . . . . . . . . 55
3.4.3 Gas-to-luminosityratiosofgalaxies . . . . . . . . . . . . . . . 57
3.5 TheevolutionofgalaxiesintheSFRvs. stellarmassplane . . . . . . 59
3.5.1 Thelocalstarformationrate-stellarmassplane . . . . . . . . 59
3.5.2 ComparisonwithobservationsoftheSFR-M planeatz = 0 . 64
⋆
3.5.3 TheSFR-M relationathighredshift . . . . . . . . . . . . . . . 68
⋆
3.6 Discussionandconclusions . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Cosmicevolutionoftheatomicandmoleculargascontentofgalaxiesand
scalingrelations 75
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Modellingthetwo-phase coldgasingalaxies . . . . . . . . . . . . . . 78
4.2.1 Darkmatterhalomergertrees . . . . . . . . . . . . . . . . . . 79
ii
4.2.2 Galaxyformationmodels . . . . . . . . . . . . . . . . . . . . . 80
4.2.3 Theinterstellarmediumandstarformationingalaxies . . . . 81
4.2.4 Consistentcalculationorpostprocessing? . . . . . . . . . . . . 85
4.3 Scaling relations for the atomic and molecular contents of galaxies
inthelocaluniverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 ThedependenceofH /HIongalaxymass . . . . . . . . . . . 87
2
4.3.2 ThedependenceofH /HIongalaxymorphology . . . . . . . 89
2
4.3.3 TherelationbetweenHI,H andstellarmass . . . . . . . . . . 90
2
4.4 Atomicandmolecularhydrogenmassfunctions . . . . . . . . . . . . 94
4.4.1 Atomichydrogenmassfunction . . . . . . . . . . . . . . . . . 94
4.4.2 Molecularhydrogenmassfunction . . . . . . . . . . . . . . . . 101
4.5 EvolutionofscalingrelationsoftheH toHIratio . . . . . . . . . . . 111
2
4.6 Cosmicevolutionoftheatomicandmoleculargasdensities . . . . . 115
4.7 Summaryandconclusions . . . . . . . . . . . . . . . . . . . . . . . . . 120
5 Predictions for the CO emission of galaxies from a coupled simulation of
galaxyformationandphotondominatedregions 125
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2 ModellingtheCOemissionofgalaxies . . . . . . . . . . . . . . . . . . 130
5.2.1 Thegalaxyformationmodel . . . . . . . . . . . . . . . . . . . 130
5.2.2 TheUCL PDRcode . . . . . . . . . . . . . . . . . . . . . . . . . 139
−
5.2.3 CouplingtheGALFORMandUCL PDRcodes . . . . . . . . . . 147
−
5.2.4 The dependence of the CO-H conversion factor on galaxy
2
propertiesinGALFORM . . . . . . . . . . . . . . . . . . . . . . . 148
5.3 TheCO(1-0)emissionofgalaxiesinthelocaluniverse . . . . . . . . . 150
5.3.1 TheCO(1-0)luminosityfunction . . . . . . . . . . . . . . . . . 150
5.3.2 TheCO-to-Infraredluminosityratio . . . . . . . . . . . . . . . 152
5.4 TheCOemissionofgalaxiesinmultipletransitions . . . . . . . . . . 155
5.4.1 TheluminosityfunctionofmultipleCOlines . . . . . . . . . . 155
5.4.2 TheCO-to-IRluminosityratioandtheCOSLED . . . . . . . . 160
iii
5.5 Assessing therobustnessofthemodelpredictions . . . . . . . . . . . 172
5.6 PredictivepoweroftheGALFORM+UCL PDRmodel . . . . . . . . . . 178
−
5.6.1 BzKgalaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.6.2 Lyman-breakgalaxies . . . . . . . . . . . . . . . . . . . . . . . 184
5.7 Discussionandconclusions . . . . . . . . . . . . . . . . . . . . . . . . 193
6 A dynamical model of supernova feedback: gas outflows from the inter-
stellarmedium 197
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.2 Thegalaxyformationmodel . . . . . . . . . . . . . . . . . . . . . . . . 201
6.2.1 TheoriginalparametrisationoftheoutflowrateinGALFORM . 203
6.3 Modellingsuperbubbleexpansiondrivenbysupernovae . . . . . . . 204
6.3.1 Theadiabaticexpansion . . . . . . . . . . . . . . . . . . . . . . 209
6.3.2 Pressure-drivensnowploughexpansion . . . . . . . . . . . . . 213
6.3.3 Momentum-drivensnowploughexpansion . . . . . . . . . . . 215
6.3.4 Bubbleconfinementandbreak-out . . . . . . . . . . . . . . . . 216
6.4 Propertiesofmolecularcloudsandthediffusemediumingalaxies . 217
6.4.1 Molecularcloudproperties . . . . . . . . . . . . . . . . . . . . 221
6.4.2 Propertiesofthepervasiveinterstellarmedium . . . . . . . . 224
6.5 Starformationequations . . . . . . . . . . . . . . . . . . . . . . . . . . 226
6.6 Towardsanewparametrisationoftheoutflowrate . . . . . . . . . . . 229
6.6.1 Radialprofileofthemassloadingfactor . . . . . . . . . . . . . 230
6.6.2 Dependenceoncircularvelocity: momentumvs. energydriven
windmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
6.6.3 Anewparametrisationoftheoutflowrate . . . . . . . . . . . 239
6.6.4 Testingtheeffectofgravity,themultiphasemediumandmetal-
licityontheexpansionofbubbles . . . . . . . . . . . . . . . . 245
6.6.5 Thephysicalregimesofsupernovafeedback . . . . . . . . . . 247
6.6.6 Comparisonwithobservationsandnon-cosmologicalhydro-
dynamicalsimulations . . . . . . . . . . . . . . . . . . . . . . . 249
iv
6.7 DiscussionandConclusions . . . . . . . . . . . . . . . . . . . . . . . . 253
7 Conclusions 257
7.1 Futuredirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
A Non-exponentialstarformationlawsandtheirapplicationtoanumerical
model 265
A.1 Numericalintegrationofthestarformationequations . . . . . . . . . 265
A.1.1 TheinstantaneousSFR . . . . . . . . . . . . . . . . . . . . . . . 265
A.2 AnIllustrationoftheimpactofapplyingdifferentstarformationlaws267
A.3 Thestarformationlaws . . . . . . . . . . . . . . . . . . . . . . . . . . 269
A.3.1 ThecriticalsurfacedensityoftheK98starformationlaw . . . 269
A.3.2 Themidplanehydrostaticpressureofdiskgalaxies . . . . . . 270
A.3.3 TheKMTstarformationlaw . . . . . . . . . . . . . . . . . . . 270
A.3.4 ExamplesofΣ surfacedensityprofiles . . . . . . . . . . . . 271
SFR
A.4 Otherobservedpropertiesofgalaxies . . . . . . . . . . . . . . . . . . 275
A.4.1 Thegalaxyluminosityfunction . . . . . . . . . . . . . . . . . . 275
A.4.2 Galaxysizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
B TheCOlineandIRluminosity 281
C Radialprofilesofthestellaranddarkmattercomponents 285
D Therecyclefractionandyieldofdifferentstellarpopulations 289
v