Modeling Physical Processes at Galactic Scales and Above

87 Pages·2014·7.93 MB·English

Modeling Physical Processes at Galactic Scales
and Above
NickolayY.Gnedin
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NickolayY.Gnedin
Particle Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA,
e-mail:[email protected];KavliInstituteforCosmologicalPhysicsandDepartmentofAs-
tronomy&Astrophysics,TheUniversityofChicago,Chicago,IL60637USA
1

Contents
ModelingPhysicalProcessesatGalacticScalesandAbove ............. 1
NickolayY.Gnedin
1 InLieuofIntroduction..................................... 4
2 PhysicsoftheIGM........................................ 5
2.1 LinearHydrodynamicsintheExpandingUniverse...... 5
2.2 Lyman-α Forest................................... 7
2.3 ModelingtheIGM................................. 16
2.4 WhatObservationsTellUs.......................... 17
3 FromIGMtoCGM ....................................... 24
3.1 LargeScaleStructure .............................. 24
3.2 HowGasGetsOntoGalaxies ....................... 26
3.3 CoolStreams ..................................... 27
3.4 GalacticHalos .................................... 29
3.5 Diversion:Coolingofrarefiedgases.................. 31
3.6 BacktoGalacticHalos ............................. 37
4 ISM:GasInGalaxies...................................... 41
4.1 GalaxyFormationLite ............................. 41
4.2 GalacticDisks .................................... 43
4.3 Ionized,Atomic,andMolecularGasinGalaxies ....... 47
4.4 MolecularISM.................................... 55
5 StarFormation ........................................... 66
5.1 Kennicutt-SchmidtandAll,All,All .................. 66
5.2 ExcursionSetFormalisminStarFormation............ 72
6 StellarFeedback .......................................... 75
6.1 WhatEscapesfromStars ........................... 75
6.2 UnconventionalMarriage:FeedbackandStarFormation. 79
6.3 TowardTheFuture ................................ 82
7 AnswersToBrainTeasers .................................. 84
References..................................................... 85
3
1 InLieuofIntroduction
What should these lectures be? The subject assigned to us is so broad that many
bookscanbewrittenaboutit.So,inplanningtheselecturesIhadseveraloptions.
One would be to focus on a narrow subset of topics and to cover them in great
detail.Suchasubsetnecessarilywouldbehighlypersonalandusefultoafewread-
ersatbest.Anotheroptionwouldbetogiveaveryshallowoverviewofthewhole
field,butthenitwon’tbeverymuchdifferentfromahighlycompressedversionof
auniversitycourse(whichanyonecantakeiftheywishso).
So,IdecidedtobeselfishandtopreparetheselecturesasifIwasteachingmy
owngraduatestudent.Givenmyresearchinterests,Iselectedwhatthestudentwould
need to know to be able to discuss science with me and to work on joint research
projects.So,thestorypresentedbelowisbothpersonalandincomplete,butitdoes
coverseveralsubjectsthatarepoorlyrepresentedintheexistingtextbooks(ifatall).
SomeoftopicsIfocusonbelowarecloselyconnected,othersaredisjoint,some
arejustsidedetoursonspecifictechnicalquestions.Thereisanoverlappingtheme,
however.Ourgoalistofollowthecosmicgasfromlargescales,lowdensities,(rel-
atively)simplephysicstoprogressivelysmallerscales,higherdensities,closerrela-
tiontogalaxies,andmorecomplexanduncertainphysics.So,we(you-thereader,
andme-theauthor)aregoingtofollowa“yellowbrickroad”fromthegaswellbe-
yondanygalaxyconfinestotheactualsitesofstarformationandstellarfeedback.
On the way we will stop at some places for a tour and run without looking back
throughsomeothers.So,theroadwillbeuneven,butIhopethatsomereadersfind
ituseful.
2 PhysicsoftheIGM
Mostofthevolumeoftheuniverseisoccupiedbygasoutsidegalaxies,theso-called
intergalacticmedium(IGM).Itmayseemthisgasislocatedfarfromgalaxies,and
shouldnotberelevanttoformationofgalaxiesandstars.Wrong!-IGMisthegas
that eventually gets accreted by galaxies and turns into stars. After all, before the
firstgalaxyformed,thewholeuniversewasjustIGM.
Hence,aswefollowthe“yellowbrickroad”toourgoalofmodelingstarforma-
tioningalaxies,wepassthroughtheIGMlandfirst...
2.1 LinearHydrodynamicsintheExpandingUniverse
Linear dynamics of the non-relativistic cold dark matter is almost trivial, density
fluctuation δ (t,k) with a spatial wavenumber k satisfies a simple ordinary differ-
X
entialequation(ODE),
d2 d
δ (t,k)+2H δ (t,k)=4πGρ¯δ (t,k), (1)
dt2 X dt X tot
where a(t) is the cosmic scale factor, H(t) a˙/a is the Hubble parameter and ρ¯
≡
is the mean density of the universe. If the universe only contained cold dark mat-
ter, then δ =δ . A second order ODE has two solutions, one of them is always
tot X
growingwithtime,
δ (t,k)=D (t)δ (k), (2)
X + 0
whereD iscalled”thelineargrowingmode”.
+
In reality, the universe contains gas, which is also subject to pressure forces.
Hence, in the linear regime the evolution of the dark matter and gas fluctuations
(δ ,δ )isdescribedbyasystemoftwocoupledequations,
X B
d2δ dδ
X +2H X =4πGρ¯(f δ +f δ ), (3)
dt2 dt X X B B
d2δ dδ c2
B +2H B =4πGρ¯(f δ +f δ ) Sk2δ , (4)
dt2 dt X X B B −a2 B
where f 0.84and f 0.16arethemassfractionsofdarkmatterandbaryons
X B
≈ ≈
respectively,andc isthespeedofsoundinthegas.
S
Thissystemofequationsiscoupled,butifhighprecisionisnotrequired,onecan
assume f f and ignore the baryonic contribution in the gravity terms in both
B X
(cid:28)
equations. In that case the solution for the dark matter fluctuation is still given by
equation(2),whiletheequationforthebaryonicfluctuationreducesto
d2δ dδ c2
B +2H B =4πGρ¯δ Sk2δ . (5)
dt2 dt X−a2 B
Notice the difference between this equation and an equation for baryonic fluctua-
tions in a static reference frame (a=const, no expansion of the universe) in the
absenceofdarkmatter:
d2δ c2
B =4πGρ¯δ Sk2δ .
dt2 B−a2 B
Weknowthatinthelattercasethecharacteristicscaleoverwhichbaryonicfluctua-
tionsaresuppressedbythepressureforceistheJeansscale,
a (cid:112)
k 4πGρ¯.
J
≡ cS
Equation (5) cannot be solved analytically in a general case, but the important
physicsweareafterishowbaryonicfluctuationsdeviatefromthedarkmatterones.
Hence,aquantityofinterestistheratiooftwofluctuations,whichcanbeexpanded
intheTaylorseriesofpowersofk2,
δ (t,k) k2
B =r +O(k4), (6)
δX(t,k) −kF2
where r =const and we will call k (t) a filtering scale. Because dark matter is
F
expectedtobemoreclusteredthatbaryons(itisnotasubjectofthepressureforce
inthelinearregime),wecanexpectthat,inageneralcasek >k (inthepresence
F J
of dark matter baryonic fluctuations are less suppressed than in a purely baryonic
case).
Inthefollowingwewillonlyconsiderthecaseofr=1(baryonstracethedark
matteronlargescales),sincethisisanexcellentapproximationforz<10.However,
at higher redshifts this is not the case any more (Naoz & Barkana, 2007), as the
different evolution of baryons and dark matter during the recombination epoch is
notcompletelyforgottenatthesehighredshifts(forexample,r 1atz>1000).
(cid:28)
Substitutingequation(6)into(5),itispossibletoobtainanexpressionfork in
F
aclosedform(Gnedin&Hui,1998),
1 1 (cid:90) t D¨ (t )+2H(t )D˙ (t )(cid:90) t dt
= dt a2(t ) + (cid:48) (cid:48) + (cid:48) (cid:48)(cid:48) .
kF2(t) D+(t) 0 (cid:48) (cid:48) kJ2(t(cid:48)) t(cid:48) a2(t(cid:48)(cid:48))
Whilethisexpressionislongandugly,forreasonablethermalhistoriesoftheuni-
verse a good rule of thumb at z 2 4 is k 2 k (the filtering scale is about
F J
∼ − ≈ ×
halftheJeansscale).
Figure 1 gives an example of scale-dependence of δ (t,k)/δ (t,k) for a repre-
B X
sentativethermalhistoryoftheuniverseatseveralredshifts(seeGnedinetal.,2003,
for details). Fluctuations on small scales, where the pressure force dominates, are
simplesoundwaves,andthetransitiontothebaryons-trace-the-dark-matterregime
iswelldescribedbythefilteringscale.
Fig.1 Solutionstoequations
(4)forarepresentativether-
malhistoryoftheuniverse
atz=4(lightgray),z=1.5
(mediumgray),andz=0
(darkgray);thinlinesshow
the exact solutions, thick
lines give the approxima-
tionδB/δX =exp(−k2/kF2)
(adoptedfromGnedinetal.
(2003)).
Brain teaser #1: Pressure generates sound waves, and sounds waves in the
ideal gas do not dissipate. Why, then, are fluctuations ”suppressed” by the
pressureforce?
2.2 Lyman-α Forest
AwellknownempiricalfactisthattheIGMishighlyionizedatlowandintermedi-
ateredshifts,z<6(wewillcomebacktothatfact).Tokeepthecosmicgasionized,
theuniversemustbefilledwithionizingradiation,theso-called“CosmicIonizing
Background”(CIB).
SincemostoftheIGMishydrogen,letusconsiderhydrogenfirst.Theionization
balanceequationforhydrogenintheexpandinguniverseissimple,
n˙ = 3Hn n Γ+R(T)n n ,
HI HI HI e HII
− −
where n , n , and n are number densities of neutral hydrogen, ionized hydro-
HI HII e
gen, and free electrons respectively, Γ is the photoionization rate and R(T) is a
(temperature-dependent)recombinationcoefficient.
Oftenitismoreconvenienttoconsidernottheactualnumberdensityofneutral
orionizedhydrogen,buttheneutralfractionx n /n ,becausethentheHubble
HI H
≡
expansiontermcancelsout,
Fig.2 Typicalz 3quasarspectrumtogetherwiththepowerlawcontinuumfit(dashedredline)
∼
andthelocalcontinuumfit(blueline;adoptedfromDall’Aglioetal.(2008)).
x˙= xΓ+R(T)n (1 x). (7)
e
− −
Intheionizationequilibriumx˙=0,hence
R(T)
x = n (1 x ),
eq e eq
Γ −
andsincetheIGMishighlyionized(x 1),
(cid:28)
R(T)
x = (n¯ +2n¯ )(1+δ),
eq H He
Γ
whereweassumedthatHeliumisfullyionized,n¯ =n¯ +2n¯ (densergasismore
e H He
neutral).
Letusnowconsideralightsourcesomewhereintheuniverse(aquasar,agalaxy,
agamma-rayburst,etc);thelightsourceisatredshiftz inourreferenceframe.Let
e
us also imagine that a photon with wavelength λ is emitted by the source. As it
e
propagatesthroughtheuniverse,thephotonisgoingtoberedshifted.Ataredshift
z <z (fromourreferenceframe)thephotonhasawavelength
a e
1+z
a
λ .
e
1+z
e
Hence,forany1216A˚(1+z )<λ <1216A˚ thereissuchz that
e e a
1+z
λ a =1216A˚.
e
1+z
e
When a photon with wavelength of 1216A˚ (= Lyman-α) hits a neutral hydrogen
atom,itcangetabsorbedandexcitetheatomton=2level.
Fig.3 Runsofneutralhydrogendensity(bottom)andgastemperature(middle)alongonelineof
sightinanumericalsimulationofLyman-α forestatz 3.Theresultantabsorptionspectrumis
∼
showninthetoppanel.
Indeed,thisisexactlywhathappensintherealuniverse.Figure2showsaspec-
trumofatypicalz 3quasar.ThebroademissionlineinthemiddleistheLyman-α
∼
ofthequasaritself,andblueenvelopefortheobservedspectrumisthecontinuum-
i.e.thelightthatthequasaritselfemitted.Blackabsorptionlinescomefromthegas
betweenusandthequasar,andthenumerousforestofthematshorterwavelength
isthehydrogenLyman-α absorptionfromtheneutralgasintheIGM,theso-called
Lyman-α Forest.
Figure 3 illustrates how fluctuations in the neutral hydrogen density and in the
gas temperature combine to produce the Lyman-α forest of absorption features in
thespectrum.Inordertounderstandhowonegoesfromthelowertwopanelstothe
top one in that figure, we need to refresh the basics of resonant line absorption in
theexpandinguniverse.
Brainteaser#2:Hydrogenatomsdonotsitforeverinn=2state,theydecay
backinton=1andaLyman-α photonisre-createdback.Howcantherebe
anyLyman-α absorption?
2.2.1 IntroductionToResonantLineAbsorption
Thecross-sectionforanatomatresttoabsorbaphotoninthefrequencyrangefrom
ν toν+∆ν totheenergylevelwiththeenergyhν is
0
πe2
σ(ν)= fφ(ν) σ φ(ν),
0
mecν0 ≡
where f istheoscillatorstrengthforthetransitionand
1 wν
φ(ν)= 0 ν δ(ν ν ),
π (ν ν0)2+w2 ≈ 0 − 0
−
where w is the natural line width in frequency units. For hydrogen Lyman-α the
combinationoffundamentalconstants
πe2
σ = f =4.5 10 18cm2.
0 −
mecν0 ×
Atoms, though, are social creatures and rarely live alone. For a cloud of gas of
densityn,sizeL,andtemperatureT weneedtointegrateoverallatomstocompute
theopticaldepthofthetransitionatanyfrequencyν,
(u u)2
(cid:90) 1 ν− (cid:48)
τ(ν)=nL σ φ(ν ) e− b2 du,
0 (cid:48) (cid:48)
√πb
whereν =ν (1+u/c)andu isdefinedviatheexpressionν=ν (1+u /c).The
(cid:48) 0 (cid:48) ν 0 ν
quantity
(cid:18) k T(cid:19)1/2
B
b= 2
m
H
iscalledtheDopplerparameterandtheproductnListhecolumndensity.
In an expanding universe it is not enough just to multiply by the cloud size L,
sincedifferentlocationsalongtheline-of-sightareredshiftedrelativetotheobserver
and project to different locations in the velocity (or frequency) space. Hence, we
mustintegratealongtheline-of-sight,
(u u )2
λ x
τ(λ)=σ0(cid:90) n(x) c e− −b2x dx , (8)
√πbx 1+zx