LectureLecture 4:4: DarkDark MatterMatter inin GalaxiesGalaxies OutlineOutline
WhatWhat isis darkdark matter?matter? HowHow muchmuch darkdark mattermatter isis therethere inin thethe Universe?Universe? EvidenceEvidence ofof darkdark mattermatter ViableViable darkdark mattermatter candidatescandidates TheThe coldcold darkdark mattermatter (CDM)(CDM) modelmodel ProblemsProblems withwith CDMCDM onon galacticgalactic scalesscales AlternativesAlternatives toto darkdark mattermatter WhatWhat isis DarkDark Matter?Matter?
Dark Matter Luminous Matter FirstFirst detectiondetection ofof darkdark mattermatter
FritzFritz ZwickyZwicky (1933):(1933): DarkDark mattermatter inin thethe ComaComa ClusterCluster HowHow MuchMuch DarkDark MatterMatter isis ThereThere inin TheThe Universe?Universe?
ΩΩ == ρρ // ρρ Μ Μ c ~2% RecentRecent measurements:measurements: (Luminous) Ω ∼ 0.25, Ω ∼ 0.75 ΩΜ ∼ 0.25, Ω Λ ∼ 0.75 ΩΩ ∼∼ 0.0050.005 Lum ~98% (Dark) HowHow DoDo WeWe KnowKnow ThatThat itit Exists?Exists?
CosmologicalCosmological ParametersParameters ++ InventoryInventory ofof LuminousLuminous materialmaterial DynamicsDynamics ofof galaxiesgalaxies DynamicsDynamics andand gasgas propertiesproperties ofof galaxygalaxy clustersclusters GravitationalGravitational LensingLensing DynamicsDynamics ofof GalaxiesGalaxies II
Galaxy ≈ Stars + Gas + Dust + Supermassive Black Hole + Dark Matter DynamicsDynamics ofof GalaxiesGalaxies IIII
Visible galaxy
Observed
Vrot
Expected R
R Dark matter halo Visible galaxy DynamicsDynamics ofof GalaxyGalaxy ClustersClusters
Balance between kinetic and potential energy → Virial theorem: v2 R M = vir G HotHot GasGas inin GalaxyGalaxy ClustersClusters
High mass required to keep the hot gas from leaving the cluster!
If gas in hydrostatic equilibrium → Luminosity and temperature profile → mass profile X-ray gas, T=10 7—10 8 K GravitationalGravitational LensingLensing GravitationalGravitational LensingLensing IIII BaryonicBaryonic andand NonNon --BaryonicBaryonic DarkDark MatterMatter II Baryons: Ordinary matter made out of three quarks, like protons and neutrons BBNS modelling + measurements of primordial abundances → Ω ≈ 0.04 or CMBR analysis baryons Ω ≈ → Baryonic 0.04
Ω ≈ → Non-baryonic 0.21
Ω Ω Ω ≈ M = Baryonic + Non-baryonic 0.25 BaryonicBaryonic andand NonNon --BaryonicBaryonic DarkDark MatterMatter IIII StillStill missingmissing inin thethe locallocal Universe:Universe: AboutAbout 1/31/3 ofof thethe baryonsbaryons →→ ΩΩ DM, baryonic ~~ 0.0150.015 ButBut note:note: TheThe missingmissing baryonsbaryons maymay havehave beenbeen detecteddetected atat highhigh redshiftredshift EssentiallyEssentially allall ofof thethe nonnon --baryonsbaryons →→ ΩΩ ΩΩ DM, non -baryonic ~~ 0.210.21 (assuming(assuming M=0.25)=0.25) MACHOsMACHOs andand WIMPsWIMPs
MACHOMACHO == MAssiveMAssive CompactCompact HaloHalo ObjectObject WIMPWIMP == WeaklyWeakly InteractingInteracting MassiveMassive ParticleParticle
But beware of misconceptions! AA FewFew ViableViable DarkDark MatterMatter CandidatesCandidates Baryonic Non-baryonic * • Faint stars • Supersymmetric particles
• Fractal H 2 • Axions • Warm/hot intergalactic gas • Sterile neutrinos • Hot gas around galaxies • Primordial black holes • Rydberg matter • Preon stars • Quark nuggets • Mirror matter • Matter in parallel branes • Kaluza-Klein particles * or evading current constraints on the cosmic baryon density HotHot andand ColdCold DarkDark MatterMatter
HotHot DarkDark MatterMatter (HDM)(HDM) RelativisticRelativistic atat decouplingdecoupling
ColdCold DarkDark MatterMatter (CDM)(CDM) NonNon --relativisticrelativistic atat decouplingdecoupling TheThe standardstandard modelmodel forfor thethe nonnon -- baryonicbaryonic darkdark mattermatter SuccessfulSuccessful inin explainingexplaining thethe formationformation ofof largelarge scalescale structurestructure AdditionalAdditional AssumedAssumed CDMCDM PropertiesProperties
CollisionlessCollisionless –– interactsinteracts mainlymainly throughthrough gravitygravity DissipationlessDissipationless –– cannotcannot coolcool byby radiatingradiating photonsphotons LongLong --livedlived particlesparticles BehavesBehaves asas perfectperfect fluidfluid onon largelarge scalesscales AdiabaticAdiabatic primordialprimordial densitydensity perturbations,perturbations, followingfollowing aa scalescale --invariantinvariant powerpower spectrumspectrum ProblemsProblems withwith CDMCDM
DarkDark halohalo densitydensity profilesprofiles DarkDark halohalo substructuresubstructure DarkDark halohalo massmass functionfunction inin thethe fieldfield DarkDark halohalo shapesshapes TheThe angularangular momentummomentum problemproblem DarkDark HaloHalo DensityDensity ProfilesProfiles II
Dark halo Visible galaxy
Log Vrot Density
Radius Log Radius Spectroscopy → Rotation Curve → Halo Density Profile DarkDark HaloHalo DensityDensity ProfilesProfiles IIII
Predicted by the Cold Dark Matter Scenario (density cusp)
Favoured by observations (density core) DarkDark HaloHalo DensityDensity ProfilesProfiles IIIIII
ButBut therethere areare plentyplenty ofof complicationscomplications …… NonNon --sphericalspherical darkdark mattermatter halos?halos? CentralCentral partpart dominateddominated byby darkdark baryonsbaryons insteadinstead ofof CDM?CDM? BestBest targettarget galaxiesgalaxies dodo notnot sitsit inin typicaltypical darkdark halos?halos? NN--bodybody simulationssimulations responsibleresponsible forfor thethe predictedpredicted CDMCDM halohalo profileprofile predictionprediction notnot reliable?reliable? DarkDark HaloHalo SubstructureSubstructure II
The dark halos around galaxies form the merger of smaller halos, but many remnants of the smaller halos survive → The dark halos of galaxies are not perfectly smooth!
≤ × Msubhalos 0.1 Mhalo
DarkDark HaloHalo SubstructureSubstructure IIII Should not dwarf galaxies form inside the subhalos?
Naïve expectation Observed A factor of 10—100 too few satellite galaxies around the Milky Way! DarkDark HaloHalo SubstructureSubstructure IIIIII
TheThe solution:solution: DarkDark galaxies?galaxies? DarkDark galaxy:galaxy: AA darkdark subhalosubhalo whichwhich eithereither lackslacks baryons,baryons, oror insideinside whichwhich thethe baryonsbaryons formform veryvery fewfew starsstars PossiblePossible detectionsdetections exist:exist: GalaxiesGalaxies withwith veryvery highhigh massmass --toto --lightlight ratiosratios PossiblePossible gravitationalgravitational lensinglensing detectionsdetections HowHow toto detectdetect halohalo substructuresubstructure II Searching for ultrafaint galaxies around the Milky Way using the SDSS → Lots of very faint galaxies found
But: Not enough of them to confirm the CDM predictions… HowHow toto detectdetect halohalo substructuresubstructure IIII Dark halos can cause image splitting in quasars on angular angular scales of ~1 arcsecond (strong lensing or macrolensing)
Observer Multiply-imaged Quasar Lens galaxy (with dark halo) HowHow toto detectdetect halohalo substructuresubstructure IIIIII Halo substructure can cause additional magnification and possibly splitting of each image. The splitting is predicted to occur on angular scales of ~0.001 arcseconds (millilensing).
Halo substructure
Macrolesing (1”) Millilensing (~0.001”)
Zoom-in HowHow toto SearchSearch forfor thethe DarkDark MatterMatter
GravitationalGravitational microlensingmicrolensing byby MACHOsMACHOs WIMPWIMP directdirect detectiondetection RecoilRecoil inin detectordetector AnnularAnnular modulationmodulation WIMPWIMP indirectindirect detectiondetection CosmicCosmic raysrays fromfrom annihilatingannihilating WIMPsWIMPs NeutrinosNeutrinos fromfrom WIMPWIMP annihilationannihilation inin Sun/EarthSun/Earth PhotonsPhotons (gamma,(gamma, radio)radio) fromfrom WIMPWIMP annihilationannihilation inin thethe GalacticGalactic CentreCentre GravitationalGravitational MicrolensingMicrolensing byby MACHOsMACHOs
LIGHT SOURCE
Obs! Fel bild! PossiblePossible detectionsdetections ofof MACHOsMACHOs MACHOMACHO project:project: monitoringmonitoring ofof 1212 ××1010 6 starsstars inin thethe LargeLarge MagellanicMagellanic CloudCloud LMC
MACHO
Milky Way
-1 DetectionDetection ofof MM compact ~10~10 MMsolar , constitutingconstituting ≈≈20%20% ofof thethe darkdark halohalo AlternativesAlternatives toto CDMCDM
WarmWarm darkdark mattermatter MixedMixed darkdark mattermatter (cold(cold ++ hot)hot) SelfSelf --interactinginteracting darkdark mattermatter SelfSelf --annihilatingannihilating oror decayingdecaying darkdark mattermatter FuzzyFuzzy darkdark mattermatter AlternativeAlternative theoriestheories ofof gravitygravity DoDo WeWe HaveHave thethe CorrectCorrect TheoryTheory ofof Gravity?Gravity? ”I invite the reader (...) to test whether he/she is not left with some uneasiness as our wonderful 'standard' cosmology seems in fact to be so far essentially based on a) a Dark Matter we do not detect b) a Dark Energy we do not understand c) a fraction of Baryons we cannot completely find! Yet everything seems to work; isn't this reminiscent of epicycles? “ L. Guzzo (2002) MONDMOND ((MOdifiedMOdified NewtonianNewtonian Dynamics;Dynamics; MilgromMilgrom 1984)1984)
Newtonian dynamics: a=MG/r 2 2 2 MOND: a /a 0=MG/r in the limit of small accelerations → µ 2 (a/a 0)a=MG/r where µ(x) ≈ 1 when x » 1 µ(x) ≈ x when x « 1 Remarkably successful in explaining the dynamics of galaxies! MONDMOND IIII
From Stacy McGaugh’s homepage:
”’You do not know the Power of the Dark Side. Join me, and together we can use dark matter to make galaxy rotation curves flat.’ I often hear this sort of paternalistic line from well intentioned senior astronomers. My response is the same as Luke's, with analogous consequences for my career.” ProblemsProblems withwith MONDMOND
OriginalOriginal MOND:MOND: PhenomenologicalPhenomenological extensionextension ofof NewtonianNewtonian gravitygravity →→ NoNo predictionspredictions forfor e.g.e.g. gravitationalgravitational lensinglensing oror cosmiccosmic expansionexpansion Solved by Bekenstein (2004)! FailsFails toto explainexplain thethe dynamicsdynamics ofof galaxygalaxy clustersclusters (e.g.(e.g. thethe famoursfamours ““BulletBullet clustercluster ””)) –– somesome darkdark mattermatter isis stillstill requiredrequired FailsFails toto explainexplain differencedifference betweenbetween systemssystems ofof similarsimilar baryonicbaryonic masses,masses, e.g.e.g. globularglobular clustersclusters andand dwarfdwarf galaxiesgalaxies ProblemsProblems inin explainingexplaining observedobserved gravitationalgravitational imageimage splittingsplitting But: Other alternative theories of gravity (e.g. MOG) may do better! SummarySummary
TheThe naturenature ofof darkdark mattermatter isis oneone ofof thethe greatgreat unsolvedunsolved problemsproblems ofof cosmologycosmology AstronomicalAstronomical observationsobservations cancan constrainconstrain thethe propertiesproperties ofof darkdark mattermatter ObservationsObservations onon galacticgalactic scalesscales seemseem toto contradictcontradict thethe CDMCDM modelmodel
Identifying the dark matter particle will probably get you the Nobel prize!