Lecture Angular Momentum

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1 Lecue Angula Momenum Tidal-Toue Theoy Halo spin Angula-momenum disibuion wihin halos Gas Condensaion and Disk Fomaion The AM Poblems Thin disk, hick disk, bulge

3 Disk Size Spin paamee Consevaion of specific angula momenum λ ~ J / M RV cons. = J / M ~ λ Rviial V ~ R disk V R R disk viial ~ λ J/M R V

4 Tidal-Toue Theoy TTT Peebles 1976 Whie 1984

5 N-body simulaion of Halo Fomaion

6 N-body simulaion of Halo Fomaion

7 Oigin of Angula Momenum Tidal Toue Theoy TTT: Peebles 1976 Whie 1984 Γ poo-galaxy peube Resul: J i ε ijk T jl I lk Tidal: T ij = i 2 φ j Ineia: I ij 3 0 Γ = a d ρ 0 i j 3

8 Tidal-Toue Theoy Halo Poo-halo: a Lagangian pach

9 Tidal-Toue Theoy d V v R L cm cm = Euleian 3 ] [ ] [, γ ρ angula momenum in Euleian pach 1 / / ax v a x ρ ρ δ & x x d X x x a L cm 3 3 ] ][, [1 & + = γ δ ρ comoving coodinaes cons. in m.d.,, S x x = d x d J x acobian , ], [ 1 = + = + δ δ Γ + = Lagangian , ], [ d S S S a L & ρ displacemen fom Lagangian o Euleian x lamina flow aveage ove in _ S S D a G D S & // ] /[4,, 2 gav = = ρ π ϕ φ φ d a D a L Γ = ϕ ρ & Zel dovich appoximaion j i j i i i + + = = φ φ φ φ 2 nd -ode Taylo expansion of poenial abou cm =0 D D a 2 3/ 2 & in a fla univese in EdS 0 2 = = cm l j jl D φ lk jl ijk i I D D a L ε 2 & = ε ijk d a I k l lk ρ 0 Γ Defomaion enso Ineia enso anisymmeic enso

10 L i = a D ε 2 & ijk T jl Tidal-Toue Theoy I lk D jl 2 φ j l = cm = 0 I lk 3 ρ 0 a0 l Γ k d 3 ε ijk Defomaion enso Ineia enso anisymmeic Tidal enso = Shea enso T D D δ / 3 Quadupola Ineia I ij I ii δij / 3 ij ij ii ij Only he ace-less pa conibues L by gaviaional coupling of Quadupole momen of _ wih Tidal field fom neighboing flucuaions Ṫ and I mus be misaligned. Γ L ill ~unaound peube

11 TTT vs Simulaions Pociani, Dekel & Hoffman 2002 Alignmen of T and I: Spin oiginaes fom he esidual misalignmen. Small spin!

12 TTT vs. Simulaions: Ampliude Gowh Rae Pociani, Dekel & Hoffman 02 Ampliude Diecion

13 TTT vs Simulaions: Scae Pociani, Dekel & Hoffman 2002

14 TTT pedics he spin ampliude o wihin a faco of ~2, bu i is no a vey eliable pedico of spin diecion.

15 Alignmen of I and T: Poohalos and Filamens

16 Alignmen of I and T: Poohalos and Filamens

17 Sages in Halo Fomaion

18 Spin axis and Lage-Scale Sucue TTT: J x = 2 φ y z I yy I zz J J y z = = 2 φ x z 2 φ x y I I xx xx I I zz yy I > I > xx yy I zz The spin diecion is coelaed wih he inemediae pincipal axis of he Iij enso a unaound. In a lage-scale pancake: he spin axis should end o lie in he plane.

19 Spin axis and Lage-Scale Sucue

20 Disk-Pancake Alignmen in he Local Supecluse

21 Halo Spin Paamee Fall & Efsahiou 1980 Banes & Efsahiou 1984 Seinmez e al Bullock e al. 2001b

22 Halo Spin Paamee Peebles 76: dimensionless λ J E GM 1/ 2 5/ 2 Bullock e al λ 3 4 J / M RV same fo isohemal sphee 3 1 GM E = M V 2 2 R σ σ = = 2σ 2 TTT: J deemined a unaound J & / 2 5/3 ~ a D φ0 MR0 ~ a M 2 3/ 2 a D & ~ ~ a δ ~ 2 D φ when δ ~ 1: 2 φ 0 ~ D 1 ~ a 1 3 comoving R 0 ~ M / ρ0 ~ M E 2 1 5/3 ~ M / R ~ a M Physical R 3 ~ ρ 1 M ~ a 3 M _ is consan, independen of a o M simulaions: _~0.05

23 Disibuion of Halo Spins <_> ~ 0.04 _ln_ ~ 0.5

24 Spin vs Mass, Concenaion, Hisoy _ disibuion is univesal _ coelaed wih a c, ani-coelaed wih C

25 Spin Jump in a Majo Mege Buke & D onghia 04 _ uie halos wih no ecen majo mege J ime

26 J Disibuion inside Halos Bullock e al. 2001b

27 Univesal Disibuion of J inside Halos µ j M < j = M vi µ > 1 j + j 0 j max j0 = J / M = µ 1 j b µ = 2VRλ' 0 Bullock e al. 2001b b µ µ ln1 µ 1 1 Two paamee family: spin paamee _ and shape paamee _ P -1 _-1 _

28 Disibuion of J wih adius: a powe-law pofile j~m s j /j max s s=1.3 æ0.3 M< /M v M vi

29 Disibuion of J in space Toy model: J by mino meges Tidal adius m l l = 2M 2 3 l dm d M α m[ l ] M Assume m and j ae deposied locally in a shell 2 d[ V ] dm 4π ρ j = m + V d d M, m l j M M l NFW halo j /j max j /j max s=1.3 æ0.3 M< /M v M< /M v

30 Whie & Rees 1978 Fomaion of Sella Disks and Spheoids inside DM Halos Fall & Efsahiou 1980 Mo, Mao & Whie

32 Galaxy Types: Disks and Spheoids The mophology of a galaxy is a ansien feaue dicaed by he mass acceion hisoy of is dak mae halo mos sas fom in disks; spheoids esul fom subseuen meges disks esul fom smooh gas acceion; oldes disk sas ae ofen used o dae he las majo mege even

33 Galaxy Fomaion in halos adiaive cooling cold ho mege spheoid disk acceion hhalos cold gas young sas old sas

34 Gas vesus Dak Mae Navao, Seinmez

35 Fla gaseous disk vs spheoidal DM halo

36 Disk/Bulge Fomaion gas only Navao, Seinmez

37 Disk Size Spin paamee Consevaion of specific angula momenum λ ~ J / M RV cons. = J / M ~ λ Rviial V ~ R disk V R R disk viial ~ λ J/M R V

38 Disk Pofile fom he Halo J Disibuion Assume he gas follows he halo j disibuion Assume consevaion of j duing infall fom halo o disk. In disk: lowe j a lowe M halo In disk: µ j < j = M vi µ > 1 j + j 0 M gas < j = f M < j j = V = [ GM ] M m halo 1/ 2 < j m disk j = fµ M v j j j + j d < 0 max Assume isohemal sphee No adiabaic conacion M j = V = m Σ = fµ M v + d < d = fµ M 2π v d d d + 2 max V vi d = max = 2λ' R b d v 1 / µ 1 µ

39 Disk Pofile: Shape Poblem Bullock e al. 2001b _ d [M d /R v2 ] _ d [M d /R v 2 ] /R vi /R vi

40 The Angula-Momenum Poblem Navao & Seinmez

41 The Spin Caasophe Navao & Seinmez e al. obsevaions simulaions j j

42 The spin caasophe obseved j disk Simulaed SPH Seinmez, Navao, e al.

43 Obseved j disibuion in dwafs disk halo BBS Low f bayons 0.03 Missing low j High λ bayons 0.07 Pj/j o j/j o van den Bosch, Buke & Swaes 2002

44 Ove-cooling spin caasophe Malle & Dekel 02 saellie + dynamical ficion idal sipping DM halo gas cooling Feedback can save he day

45 Obial-mege model: Add obial angula momenum in mege hisoy Mege hisoy Obi paamees Binney & Temaine and andom oienaion

46 Succes of obial-mege model model Malle, Dekel & Someville 2002 simulaions

47 Model success: j disibuion in halos simulaions model

48 Low/high-j fom mino/majo meges High-j fom majo meges simulaions J model Low-j fom mino meges

49 Supenova Feedback: V SN Dekel & Silk 86; Dekel & Woo 03 Enegy fed o he ISM duing he adiabaic phase: E SN νε M& ad M * ad ff M& M * ff 0.01 fo Λ T 1 a T ~ 10 5 K Enegy euied fo blowou: E M SN gas V 2 V 10 ci 100 km/s M ci 3 10 M o

50 Feedback in saellie halos V vi> V fb ho gas DM j b <j DM ho gas j b =j DM Vvi V fb V vi< V fb 2 blow ou j b >j DM /

51 Model vs Daa Malle & Dekel 02 BBS daa: 14 dwafs, van den Bosch, Buke & Swaes 02 bayon facion model dwafs bigh spin paamee BBS daa BBS daa model dwafs V vi =60 One fee paamee in model: V feedback 90 km s -1

52 J-disibuion wihin galaxies DM halo disk daa model BBS: van den Bosch, Buke & Swaes 2002

53 Summay: feedback effec on spin In big saellies meging o big galaxies heaing gas expansion R b ~R DM idal sipping ogehe λ ba ~ λ DM In small saellies meging o dwafs gas blowou f ba down blowou of low j gas λ ba > λ DM

54 Thin Disk and Thick Disk Navao & Seinmez

55 Dynamical Componens of a Simulaed galaxy

56 Dynamical componens of a simulaed galaxy non-oaing spheoid hick disk hin disk Obial Ciculaiy Abadi Abadi e e al al 03 03

57 Fomaion of Thick Disk Sella saellie meging wih disk: edge-on

58 Fomaion of Thick Disk Sella saellie meging wih disk: face-on

angular momentum Angular Momentum in Halos & Galaxies how do galaxies get their spin? the spin parameter

angular momentum Angular Momentum in Halos & Galaxies how do galaxies get their spin? the spin parameter Physics 46, Sping 7 Lectue 11 angula momentum Angula Momentum in Halos & Galaxies Tial toque theoy Halo spin The angula momentum istibution in halos Gas conensation & Disk fomation The AM poblems gas AM