LCDM: Successes and Challenges
Avishai Dekel
Center for Astrophysics and Planetary Science The Hebrew University of Jerusalem
Beyond WIMPs: From Theory to Detection June 2015 Astronomers have been measuring Dark Matter since 1933 (Zwicky – missing mass)
Novikov Dark Matter Halos in Galaxies
dark halo flat rotation curve v
v R R GM (R) V 2 = 3,000 light years RR → M(R) ∝ R
30,0000 ly Dark Matter
or modified gravity? DM in Galaxy Clusters: Gravitational Lensing
HST Large Scale Cosmic Flows POTENT
Great Attractor
Dekel & Bertschinger 1990 Dark Matter Density
us Large Scale3D dark matter Mass densityDistribution
Great Attractor Perseus Pisces
Great Void Most Mass is Non baryonic Dark Matter
Planck+ 2015:
Total Mass m=0.308 ± 0.012
Baryons b=0.0478 ± 0.0004 Formation of Structure History
Early Universe
Cosmic Microwave Background
Dark Ages
Galaxy Formation time Gravitational instability
small amplitude fluctuations:
ρ
gravitatinal instability:
galaxy cluster ρ void 0
The Initial Fluctuations At Inflation: Gaussian, adiabatic
r r r δ (x) = δ r e ki ⋅x Fourier transform: ∑r k k ~ r Power Spectrum: P(k) ≡ <|δ (k |) 2 > ∝ k n
kmax 2 2/1 3 −(n+ 6/)3 rms perturbation: δ rms = < δ > ∝ ∫ Pk d k ∝ M k=0
Correlation function: r r r ~ r r r ξ (r) ≡ < δ (x)δ (x + r ) > ∝ ∫|δ (k |) 2 e− ki ⋅r d 3k ∝ r −(n+ )3 dP = 1[ +ξ(r)] n dV CDM Power Spectrum of linear fluctuations
horizon M H ∝ t δ H Scale invariance: δ mass H same δ at horizon δ H δ growth when matter is self gravitating ρrad ρmass
kmax teq t0 time < δ 2 > 2/1 ∝ P d 3k ∫ k 3/2 3/2 − 3/2 k =0 δ ∝ (t / tH ) ∝ t M
CDM +1 δ Pk k M − 3/2 k −3 HDM HDM CDM free streeming
∝ Meq mass kpeak m h k Formation of Large Scale Structure
Linear fluctuation growth δ <<1 → δ ∝ a ∝ t 3/2 n + 3 rms fluctuation at mass scale M P ∝ k n → δ ∝ M −α 0 < α = ≤ 3/2 k 6 −α /1 α Typical objects forming at a: 1 ~ δ ∝ M a → M * ∝ a
CDM: bottom up HDM: top down 2 2/1 2 2/1 δρ δρ ρ ρ 1 1
free CDM streaming HDM 0 0 M M DM Particle Mass
4 4 HDM: relativistic till z eq ~10 , T~10 K > m ~ ev, 15 MH~10 M (clusters superclusters)
9 WDM: M H~10 M (small galaxies) > m ~ kev
6 CDM: M H~10 M (dwarf galaxies) > m ~ Gev Micro Macro Connection
Cold Dark Matter
Hot Dark Matter (ν) The Cosmic Web in LCDM SDSS Galaxy Redshift Survey
Cosmic Microwave Background Planck 2015: CMB Temperature Map
δT/T~10 5 arcmin ΛCDM matches in detail the CMB TT fluctuations It allows accurate parameter determination
curvature Planck 2015
initial fluctuations dark matter
baryons Polarization by scattering off electrons; re ionization by stars & quasars at z~10
Planck 2015 Success of the LCDM Power Spectum Success of the LCDM Power Spectum Standard ΛCDM Model Parameters 2015: Planck (+BAO+SN)
Total density m+λ = 1.000 ± 0.005
Dark energy density . Λ = 0.692 ± 0.012 Mass density . m = 0.308 ± 0.012 Baryon density .. b = 0.0478 ± 0.0004
1 1 Hubble constant H 0=67.8 ± 0.9 km s Mpc Age of universe t 0=13.80 ± 0.02 Gyr
Fluctuation spectral index n s=0.968 ± 0.006 Fluctuation amplitude σ8=0.830 ± 0.015 Optical depth τ =0.066 ± 0.016 Beyond the Standard ΛCDM Model 2015: Planck (+BAO+SN)
Total density tot = 1 k = 1.000 ± 0.005 Equation of state w = 1.006 ± 0.045
Tensor/scaler fluctuations r < 0.11 (95 % CL) Running of spectral index dn/dlnk = 0.03 ± 0.02
Neutrino mass ∑ m ν < 0.23 eV (95% CL) # of light neutrino families N eff =3.15 ± 0.23 Dark Matter Halos The Cosmic Web of Dark Matter
dark matter halo
the millenium cosmological simulation N body simulation of Halo Formation Spherical Collapse
ρ max ≈ 5.5 ρ universe
ρ radius vir ≈ 200 perturbation ρ
virial equilibrium
time
1 GM GM virial equilibrium: E = − = − 2 Rvir Rmax Halo Virial Scaling Relations
2 GM v Virial equilibrium: Vv = Rv
M v −3 Spherical collapse: 3 = 200 ρu = 200 ρu0 a 4( π )3/ Rv
3 2/3 3 −3 M v∝Vv a ∝ Rv a
4 To get the observed Tully Fisher Relation: L~Vdisk need only small adjustments Galaxy Formation A Recent Paradigm Shift Disks: rotating, gas and young stars, blue Spheroids: pressure support, old stars, red Hubble Deep Fields: Time Evolution
Peak of galaxy formation at z~2 4 (t=1 3 Gyr) Standard Picture: Spherical Collapse Rees & Ostriker 77, Silk 77, White & Rees 78, Fall & Efstathiou 80 …
Proto halo expansion, turnaround, collapse to a virialized DM halo – at overdensity ~ 200 AM by tidal torques prior to maximum expansion Spin λ~(J/M)/RV~0.04 independent of mass and time
Spherical gas infall into the halo 6 Virial shock heating to T v~10 K
Radiative cooling, cylindrical accretion to disk AM is conserved. Halo AM determines disk size and structure: R disk ~ λ Rhalo
Bulge by mergers & disk instability Standard Paradigm: Mergers
radiative cooling
cold
hot spheroid merger disk
accretion dark matter halos cold gas disk starburst, spheroid old stars Stellar+AGN feedback leads to red and dead Ellipticals TidalA Galaxy interaction Merger & Merger Mergers: Simulations versus Observations Cosmic web Streams AMR RAMSES (including mergers) Teyssier, Dekel feed galaxies box 300 kpc res 30 pc z = 5.0 to 2.5 Streams Feeding a High z Galaxy
Tweed, Dekel, Teyssier RAMSES Res. 50 pc 100 kpc An Extended Tilted Ring about the Disk gas density Danovich, Dekel+ 15
30 kpc stream lines
expressway entrance Clumpy Disk Ceverino, Dekel et al. 10 kpc z=4 2.1 Stream Fed Galaxies at High z
external stimulation by mergers, cold streams counter rotation, tidal compression wet compaction to “blue” nugget and black hole thick disk hot halo quenching bulge
VDI outflows SFR spheroid
clumpy disk late disk
hot halo The main mode of galaxy formation Challenges to LCDM The Tully Fisher Relation From Halo Virial Relations to Observed TF
3 2/3 4 M v∝Vv a L∝Vdisk
Massive galaxies
no outflows M ∝ M L ∝ M ∗ v ∗ 4 − 5.0 L ∝ Vdisk rotation curve shape Vdisk /Vv ∝Vv
Low mass galaxies
2 strong outflows M ∗ / M v ∝Vv -0.2 4 low mass gals are blue L/ M∗ ∝ M∗ L ∝Vdisk
Vdisk ≈Vv
Challenge: reproduce simultaneously the slope, zero point, scatter, and the luminosity function TF Relation: Simulations vs Observations
V4
EAGLE simulations Schaye+ 2015 TF Relation: Simulations vs Observations
Observations 5 McGaugh & Stark M*~V
NIHAO Simulations Wang, Dutton+ 2015
Steeper when V is measured at a larger r because V(r) is declining for massive galaxies TF Relation: Simulations vs Observations
Observations McGaugh & Stark
NIHAO Simulations
Wang, Dutton+ 2015 5 M*~V The TF slope depends on which V is used Reyes+ 2011
M~V 3.5 M~V 4.2 The Challenge in the TF Relation
Need to reproduce simultaneously the slope ~3 5 zero point small scatter ±0.2 dex and the galaxy luminosity function
Given the DM virial relations, the key for the adjustments is the systematic variations of V disk /V vir and M */M vir (or M bar /M vir )
These variations depend on halo properties, gas inflow, SFR, and especially on feedback!
Adiabatic contraction of DM must be avoided – otherwise V disk gets too high (zero point). Feedback!
The small scatter is because galaxies evolve along the relation: more gas > higher SFR > larger M * > higher V Mass Function: Galaxies vs DM Halos
Halos (Press Schechter) Scale of non linear fluctuations faint end quenching
2 2/1 MPS (a) by δ (MPS ,a) =δcollapse ≈ 7.1 M 2
halos M (a) A power law power spectrum PS n Pk ∝ k α = (3+ n) / 6≈1/ 6 M 1 M ≈10 13 M a /1 α galaxies PS Θ log n(M) exp( M1/3)
~ ~ e M n(M ) ∝ M −2+α exp( − 5.0 M 2α ) ~ M ≡ M / M PS bright end quenching
6 8 10 12 14 log M Evolution of Star Formation Rate Density
11.5 Peak in M halo ~10 M early, small mass late, high mass quenching quenching Quenching of Star Formation in Massive Galaxies Virial Shock Heating Dekel & Birnboim 2006 11.8 critical halo mass ~~10 Mʘ −1 −1 Kravtsov+ tcool slow cooling > shock in hi z massive hot halos cold streams penetrate fast cooling –> no shock Cold Streams in Big Galaxies at High z 10 14 all hot cold filaments Mvir 10 12 in hot medium Mshock ~M * [M ʘ] Mshock >>M * Mshock all cold 10 10 M* Dekel & 0 1 2 3 4 5 Birnboim 06 redshift z Shock Heating Triggers AGN Feedback M>M shock More than enough energy is available in AGNs Hot gas is vulnerable to AGN feedback, while cold streams are shielded →Shock heating is the trigger for AGN feedback in massive halos Kravtsov et al. Merger: Galaxies with a Central Black Hole Strong Feedback on Small and Large Scales Large Small and on Feedback Strong feedback 0 1 photo ionization UV UV ondust 10 9 9 10 10 10 SN M 10 cold hotcold vir vir 11 11 [M 10 ʘ ] 12 12 in groups dynamical friction 10 medium AGN + hot 13 13 10 14 Small Scale Issues Missing dwarfs / Too big to fail Cusp core Missing Dwarfs in a Milky Way Halo simulation V>30 km s 1: ~10 subhalos, 2 dwarfs V>10 km s 1: ~10 5 subhalos, ~20 dwarfs Milky Way Dwarfs Low mass Galaxies are of Low Surface Brightness DM dominated: Low M star /M DM DDO154 simulations observations Low Surface Brightness & Dwarf Galaxies The dark halo cusp/core problem −α −3+α r 0 r 0 ρ(r) = ρ s 1+ rs rs simulated cusp α≥ 1 log ρ observed core α=0 α=3 rs log r Observed Cores vs. Simulated Cusps cusp α≥ 1 V core α=0 r GM (r) V 2 = r →V ∝ r1−α 2/ Marchesini, D’Onghia, et al. The Astrophysical Solution: Feedback The baryonic mass in galaxies is ~20% of the cosmic baryon fraction Outflows are observed Supernovae Feedback Radiative Feedback No supernovae Radiative pressure by UV ionizing photons from massive young stars Acting on dense gas and dust Some IR trapping P=(L/c)/R 2 for 5 Myr Rosette Nebula 40 pc Inflows and Outflows Gas density Temperature Velocity dilute hot 11 DeGraf, Ceverino + 15 cosmological simulations 25pc z=2.6 Mv=7x10 radiative fdbk η~3 Outflows remove most of the gas Supernova Driven Outflow Dekel & Silk 1986 + Energy fed to the ISM during the “adiabatic ” phase: & ESN ≈νε M∗ trad ∝ M* (trad tff ) & ≈ 01.0 M ∗ ≈ M * tff 2 Energy required for blowout: ESN ≈ M gas V -1 10 Vcrit ≈100 km s → M ∗crit ≈ 3×10 M Θ 2 −1 M * / M v ∝V (M * << M outflow V <<100 km s ) Maximum Effect on DM if Instant Blowout GM 2 1 E = − + MV 2 before R 2 Lose M/2 while V 2 is unchanged: G(M )2/ 2 1 E = − + (M )2/ V 2 = 0 after R 2 unbound! Reaction of DM Halo to Gas Blowouts Adiabatic contraction DM gas Instant gas blowouts Puffed up by supernova feedback DM core Can TBTF be solved with supernova feedback? Governato, Pontzen+ 12 observations 6 Simulations w fdbk Small M *~10 M galaxies not enough SN energy? Slope of density profile at r=50pc Garisson Kimmel+ 13 simulations simulations observations Need the SN feedback to be more effective than previously modeled Do we need a different kind of DM to reduce the small scale power? Warm DM? Self interacting (repulsive) DM? Summary LCDM is extremely successful in matching the CMB and large scale structure Robust predictions for global properties of cosmic web and DM halos Rapid progress in implementing baryonic processes, within the cosmic web, to explain the evolution of galaxy properties: mass, size, morphology, SFR and quenching Challenges: TF relation, missing dwarfs and cusp/core. Astrophysical answer: stellar and supernova feedback (yet to be modeled in proper detail) Conclusion Do we desperately need non CDM dark matter? I don’t think so Do we know the full answers within CDM and baryonic physics Not yet, but we are on our way Will it be interesting for particle physicists to come up with non CDM DM candidates that may help with the small scale issues? Absolutely yes