Characteristic Scales in Galaxy Formation

Characteristic Scalesin Galaxy FormationAvishai DekelHU Jerusalemvisiting IAP & Observatoire de ParisParis, December 2003

Four Observed Scales• galaxies V < 300 km/s• Bi-modality: M *crit ≈3x10 10 M ʘ ~L *V~ 100 km/s- discs, blue star-forming, LSB, …- spheroids, red old-pop, HSB, AGNs, …

Bi-modality: Age vs Stellar MassSDSS Kauffmann et al. 03

Transition Scale in MetallicitySDSS Tremonti et al.

Transition in Surface Brightnessµ *SDSS Kauffmann et al. 03M * /M ʘ

Observed Scales• galaxies V < 300 km/s• Bi-modality: M *crit ≈3x10 10 M ʘ ~L *V~ 100 km/s- discs, blue star-forming, LSB, …- spheroids, red old-pop, HSB, AGNs, …• dark-dark halos (and dSph) V < 30 km/s

Dark-Dark Halos at V < 30 km/sTF: L~V 4Virial: M~V 3ψ(M) ~ M -2φ(L) ~ L -1Cannot bereconciled !#observedgalaxiespredictedhalos10 100 1000Velocity (km/s)

Observed Scales• galaxies V < 300 km/s• Bi-modality: M *crit ≈3x10 10 M ʘ ~L *V~ 100 km/s- discs, blue star-forming, LSB, …- spheroids, red old-pop, HSB, AGNs, …• dark-dark halos (and dSph) V < 30 km/s• dwarfs V > 10 km/s

Lower Bound?LG DwarfsV~10 km/sDekel & Woo 03

Observed Scales• galaxies V < 300 km/s• Bi-modality: M *crit ≈3x10 10 M ʘ ~L *V~ 100 km/s- discs, blue star-forming, LSB, …- spheroids, red old-pop, HSB, AGNs, …• dark-dark halos (and dSph) V < 30 km/s• dwarfs V > 10 km/s

Theoretical Scales: OutlineV (km/s)M * (M ʘ )M(M ʘ )Cooling (Brems.)30010 1210 13Shock heating1003x10 103x10 11Supernovae1003x10 103x10 11Photoionization3010 83x10 9Cooling (H)105x10 55x10 7

Simulations

Toy Modeling

Analytic Modeling

Semi-Analytic Modeling

Theoretical Scales: OutlineV (km/s)M * (M ʘ )M(M ʘ )Cooling (Brems.)30010 1210 13Shock heating1003x10 103x10 11Supernovae1003x10 103x10 11Photoionization3010 83x10 9Cooling (H)105x10 55x10 7

1. Cooling Scales

Standard Picture of Infall to a DiscRees & Ostriker 77, Silk 77, White & Rees 78, …Perturbed expansionHalo virializationGas infall, shock heatingat the virial radiusRadiative coolingAccretion to disc if t cool

Cooling vs Free FallRees & Ostriker 77, Silk 77, White & Rees 78T10 4 10 5 10 6 10 7+3log gasdensity+1dark mini-halos-1-3lower boundtoo small-5H 2dwarfsCDMt cool

2. Shock-Heating ScaleIs there a virial shock?Birnboim & Dekel 03

10000Growth of a Massive GalaxyT ° K1e+007100010 11 M 10 12 M 1e+006100000radius [kpc]10010shock-heated gas1000010001“disc”1000.1100 1 2 3 4 5 6 7 8time [Gyr]Spherical hydro simulation Birnboim & Dekel 03

A Less Massive GalaxyT ° K10001e+00710010 11 M 1e+006radius [kpc]101cold infallshocked“disc”1000001000010000.11000.010 1 2 3 4 5 6 7 8time [Gyr]10Spherical hydro simulation Birnboim & Dekel 03

Hydro Simulation: ~Massive M=3x10 11z=4M=3x10 11T vir =1.2x10 6R vir =34 kpcvirialshockKravtsov et al.

Less Massive M=1.8x10 10z=9M=1.8x10 10T vir =3.5x10 5R vir =7 kpccoldinfallKravtsov et al.

Cold Streams M=3x10 11z=4M=3x10 11T vir =1.2x10 6R vir =34 kpccoldstreamsKravtsov et al.

Cold Streams M=3x10 11z=4M=3x10 11T vir =1.2x10 6R vir =34 kpccoldstreamsKravtsov et al.

Cold Streams M=3x10 11z=4M=3x10 11T vir =1.2x10 6R vir =34 kpccoldstreamsKravtsov et al.

SPH: Less Massive M=1.4x10 11z=5.5M=1.4x10 11T vir =9x10 5R vir =24 kpchotstarsCold flowsalways

Gravitational Instability Below the ShockEq. of state:Adiabatic:γ =P⎛ ∂⎜⎝ ∂= ( γ −1)ρeγ = 5 / 3lnlnP ⎞ ⎟⎠ρsstable:γ > 4 / 3radius [kpc]1000010001001011e+0071e+006100000100001000100With cooling (rate q):γeffd(lnP)ρ ⎛ P&⎞≡ =d ρ P⎜& ρ⎟(ln ) ⎝ ⎠= γ −ρ q& ρ e0.10 1 2 3 4 5 6 7 8time [Gyr]t dynt coolBirnboim & Dekel 03e&= −PV&− q10In pre-shock quantities:γeff= γ −64( γ + 1)( γ −1)2ρ r Λ0s3u0( T )1T1=µk NBA2γ−1( γ + 1)2u20

Perturbation analysisr→r+ δrrestoring force: δ & r / δr = ?Assume homologous infall:ruδtur1δ = =srδt1 GMEq. of motion (sub-sonic): && r = − ∇P− = 02ρ rδr4 2−& ∝ γ − − ( γ −γeff)δr3 γStable if >0effγeff= γ −ttdyncoolStabilitycriterion:γeff2γ> γcrit= = 1.42 ( γ =γ + 2 / 35 / 3)Birnboim & Dekel 03

Gravitational Instability Below the ShockBirnboim & Dekel 03Effectiveconstant:γeff≡d(lnP)d(lnρ)= γ −ρ q& ρ e≈ γ −ttdyncoolStabilitycriterion:γeff2γ> γcrit= = 1.42 ( γ =γ + 2 / 35/ 3)

]δ(1011)=0.093timeSpherical Simulation vs Model1000 10010001052z11e+007100flow lines1e+006radius [kpc]radius [kpc]10010101virialshock1000001000010000.1 1’disc’1000.010.10 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8time [Gyr] [Gyr]2γ crit =1.42101γ critγ eff0at infallγ eff-1shock formation

Model vs. 3D simulations0.2Temperature1e+0060.2γeffPost-shock Temperature"xy" u 4:5:11e+007 1.70.150.151.6Y (/h Mpc)0.10.050-0.05-0.110000010000Y (/h Mpc)Temperature (K)0.10.050-0.05-0.11e+0061.51.41000001.31.210000-0.15-0.151.1-0.21000-0.21000 1-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2 -0.15 -0.1 -0.05 00 0.05 0.1 0.1 0.15 0.15 0.2 0.2X (/h Mpc)X (/h Mpc)

Model vs. 3D simulations0.2Temperature1e+0060.2γeff1.70.150.151.6Y (/h Mpc)0.10.050-0.05-0.110000010000Y (/h Mpc)Temperature (K)0.10.050-0.05-0.11.51.41.31.2-0.15-0.151.1-0.21000-0.21-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2X (/h Mpc)X (/h Mpc)

Critical mass for shock heating:Low Z high ZM halo ≈ (1-3) x 10 11 M ⊙M * ~(1-3)x10 10 M ⊙~ insensitive to redshiftAt z ≥ 2 most halos are M

Fraction of cold/hot accretionZ=0Z=3ffMMKeres, Katz, Weinberg, Dav’e 2004

Accretion Rate at Different TemperaturesZ=0Z=3 Z=5MT max /T virKeres, Katz, Weinberg, Dav’e 2004

Shock-heating ScaleBirnboim & Dekel 03T10 4 10 5 10 6 10 7+3M * ~3x10 10 M ʘlog gasdensity+1-1-3H 2cold infallinto discsCDMBrems.shock heatingt cool

Implications of Cold InfallModify SFR & SN feedback. Bursts?X-rayReduce soft X-ray flux.hot gasExplain the missing background?Enhance Ly-α emission.Ly-α emitters?Ly-αStromgrensphereX-rayHIIcold infall

Effect of no virial shocksBefore: after:Creates too much soft xNaturally explainsLyα emittersHot, diffuse,ionized–emits soft XCold, dense, neutral-emits LyαPen 1999, Wu et al. 2001, Benson et al 2000

Missing Soft X-ray Backgroundmodels assumingshock heatingobservedL x -T in clustersWu, Fabian & Nulsen 01

Ly-α EmittersLy-α Emittersskystargalaxy: continuum & lineManning et al. 00

Ly-α at z=4.1Miley et al.

3. Supernova Feedback ScaleDekel & Silk 86Dekel & Woo 03

Simulation of supernova blowouttimeMori et al.

Galactic wind M82

Supernova Feedback Scale(Dekel & Silk 86)Energy fed to the ISM during the “adiabatic” phase:ESN≈νεM&∗trad∝M*( tradtff)M&∗ ≈ M * t ff≈ 0.01for Λ ∝ T−1atT~ 105KEnergy required for blowout:E ≈ MSNgasV2→V10crit ≈100 km/s → M∗crit≈ 3×10 M o

Supernova Feedback ScaleDekel & Silk 86T10 4 10 5 10 6 10 7+3log gasdensity+1-1-3H 2dwarfst cool

Dekel & Silk 86LSB vs HSB

LSB vs HSBSDSSµ *M * /M ʘLocal Groupdwarfsµ *M * /M ʘM *crit ~10 10 M ʘMateo 98, Woo & Dekel 03

The “Fundamental Line” ofLSB/Dwarf Galaxies

Bright Galaxies• virial haloGMV ∝R• Mtop hatM3R∝ 200ρ2 u∗∝M• disk sizeµinitialgas ∝fbarMR∗≈ λRspin→λ ≈ const.2 −21 / 3* ∝ M * / R*∝ λ M ∗M→∝V3∝RM ∝ V∗→ µ ∝ M * *331/3• Z ∝ M * / M gas→ Z ∝const.

Model: fundamental line of LSB/Dwarfs(Dekel & Woo 03)• Energy:ESNM∝MgasV2M* / M Vgas ∝2• Virial halo:V3∝M∝R3

“Fundamental Line” of LSB/DwarfsSurfaceBrightnessSDSSLocal Groupdwarfsµ * ∝ M *0.6µ *M * /M ʘM *crit ~10 10 M ʘµ *M * /M ʘWoo & Dekel 03

MetallicityZ∝M *0.4SDSS Tremonti et al.

LG Dwarfs: MetallicitySDSSZ ∝ M *0.4datamodel

LG Dwarfs: VelocityV ∝ M *0.2TFV>10 km/sdatamodel

Summary: SN feedbackCould be responsible for thetransition scale at M * =3x10 10 ,and the “fundamental line” ofLSB/dwarf galaxies, M*/M∝V 2 .

Shock Scale ≈ Supernova ScaleT10 4 10 5 10 6 10 7+3log gasdensity+1-1-3H 2dwarfsHSBLSBcold infallinto discsM *shock ~3x10 10CDMBrems.shock heating-5t cool

vs M for halos in 2dFSupernovafeedbackShock heatingAGN feedbackUsing conditional luminosity function: Van den Bosch, Mo, Yang 03

vs M for halos in 2dFM/LSupernovafeedbackShock heatingAGN feedback10 11 12 13 14MUsing conditional luminosity function:Van den Bosch, Mo, Yang 03

Bi-Modality at M *crit ~ 3x10 10 M ʘMM critcold infall → discs (bursts?)hi-z progenitors < M crit → discsmerge to spheroids → red, oldhot gas (+ cold flows)SN feedback regulates SFR→ blue, young popM * /M∝V 2 →LSB fundamental lineAGN feedback prevents cooling?Ly-α emitters?some X-ray?

4. Photoionization ScaleEvaporation byThermal WindsShaviv & Dekel 2003

Theory: Many Sub-HalosSimulation by Moore et al.

CDM model: many dwarf satellitesMoore et al

Only a few faint dwarf satellitesM31Leo I (dSph)NGC 205 (dE)Antlia (Tr)FGC 227 (LSB)

It isn’t that simple to turn on the light

Search for Dark-Dark Halos

Dark-Dark Halos V

Complete removal of gas from proto-halos?By SN outflow? unlikelyBy ram pressure due to outflow from anearby galaxy (Scannapieco, Ferrara & Broadhurst 00) ?By radiative feedback?

Radiative FeedbackReionization of H by UV flux from stars and AGNby z ion ~10 → heating gas to T ≈(1-2)×10 4 KJeans scale – no infall into halos of V

Evaporation of hot gasρ gasrρ gasrkTφkTφcold gas hot gasMass loss from top of potential wellIt is continuously replenished and losttevap≈ tContinuous energy input by the ionizing flux→ steady winddyneφ / kT

Evaporated Mass FractionBarkana &Loeb 99instantShaviv &Dekel 03windz ion =8z end =2

Summary Dwarf HalosDark halos must exist at V

Scales SummaryT10 4 10 5 10 6 10 7log gasdensity+3+1-1-3H 2V ionization ~30totalgaslossdwarfsHSBLSBcold infallinto discsM *shock ~3x10 10CDMBrems.shock heating-5t cool

Summary: Characteristic ScalesV (km/s)M * (M ʘ )M(M ʘ )Cooling (Brems.)30010 1210 13clusters{Shock heatingSupernovae1001003x10 103x10 103x10 113x10 11L * ,discsLSBPhotoionization3010 83x10 9dSph darkCooling (H)105x10 55x10 7

Thank you

The Turkish astronomer (The Little Prince)

What do scientists really like?

Einstein predicts Hi-Tech

Newton?

Search for Dark Matter

CDM model: many dwarf satellitesMoore et al

A Low-Surface-Brightness Galaxy

Dark-Dark Halos must exist !virial, top-hat:M ∝ V3Tully Fisher:L∝Mx 3xx−1∝ V3x≈ 5→ dL / dM∝Mluminosity function:mass function:∝ − αϕ( L)L α ≈1.2ψ ( M ) ∝ M− β ≈1.8⇒ ( α−1)x =β−1−γ0 →γ .2∗≈0 5/3.5≠−0.8Cannot reconcile TF with luminosity and mass functions !βαx−β + γ( M ) dM = ϕ(L)dL → dL / dM ∝ Mf ( M )ψ ( M ) dM = ϕ(L)dL → dL / dML∝Mfraction of halos with luminous component:γf L ∝ M→f L∝ M0.5−0.8∝ V2L / M ∝ Vcompletely dark halos SN feedback2

Caveats• supernova feedback is a complex process:- asymmetric- thermal energy, bulk motion, turbulence• several bursts of star formation• blowout >> the escape velocity• gas missing also in big galaxies• do dwarfs have very massive halos?• can radiative feedback eliminate big dwarfs?• can outflows eliminate big nearby dwarfs?

Cooling rate-21log Λ mic [erg cm 3 /s]-22-23Z=0.05Z=0Line emissionZ=0.3Bremsstrahlung-244 5 6 7 8log T [K]

Observed Scales• galaxies V < 300 km/s• Bi-modality: M *crit ≈3x10 10 M ʘ ~L *V~ 100 km/s- discs, blue star-forming, LSB, …- spheroids, red old-pop, HSB, AGNs, …• dark-dark halos (and dSph) V < 30 km/s• dwarfs V > 10 km/s

TalksOct 03 Venice 30 minDec 03 IAP EARA workshop 30Dec 03 Meudon 45Dec 03 IAP 45Jan 04 ETH Zurich 45