Dark Matter Halos of Spiral Galaxies Arunima Banerjee National Centre for Radio Astrophysics Tata Institute of Fundamental Research Pune, India email: [email protected] Web: http://www.ncra.tifr.res.in/~arunima PLAN OF THE TALK • Spiral Galaxies: An Overview • Dark Matter: A Brief History • LCDM model: Success & Failure • Tracking DM halos using HI Rotation Curve & Scale height data • Application & Results • Summary Spiral Galaxies: An Overview OUR MILKY WAY OTHER SPIRAL GALAXIES NGC 891 NGC 628 THE GALAXY CLASSIFICATION SCHEME NGC 628 FACE-ON SPIRAL GALAXY NGC 891 M87 EDGE-ON SPIRAL GALAXY ELLIPTICAL GALAXY BASIC BUILDING BLOCKS OF A SPIRAL GALAXY σ MASS ∆R ∆Z (km/s) (Msun ) (KPC) (KPC) Differential Rotation DM 10 12 200 200 STARS 10 11 10 0.350 18 Caveat: Not to Scale! GAS(HI) 10 10 30 0.15 - 1 7-9 R A MULTI-WAVELENGTH VIEW OF THE MILKY WAY GALAXY ENVIRONMENT: CLUSTER, GROUP, FIELD Cluster Group Abell 1689 Field Robert’s Quartet NGC 891 Dark Matter: A Brief History DARK MATTER: CLUSTER KINEMATICS (1933) Fritz Zwicky From Virial Theorem, Coma Cluster (Abell 1669) T + V = 0 Estimable from the Doppler Shifts of the i.e. V = -T galaxy spectra Hints at the existence of Dark Matter! But Estimable from the lumininosities of the V >> Vobs !! galaxies DARK MATTER: GALAXY ROTATION CURVE (1980) Vera Rubin Observed M(R) ~ R !! VROT =(GM/R)½ R Vrot (km/s) R(kpc) DARK MATTER: LARGE SCALE STRUCTURE AND COSMOLOGY Observed Large Scale Structure (SDSS) Ansotropies in the Cosmic Microwave Background (WMAP) Abundance of H, He, Li ΛCDM: STANDARD MODEL OF COSMOLOGY ORDINARY MATTER! Matter-energy budget in the LCDM universe which consists of dark energy and cold, dissipationless and collisionless dark matter LCDM Model: Success & Failure DARK MATTER DISTRIBUTION IN THE UNIVERSE AT PRESENT TIME Millenium Simulation LCDM HALOS: A ONE-SLIDE PRIMER Bett et al. (2007) c 1. DM halos are triaxial (a > b > c) in a general b a:long axis b: intermediate axis c: short axis Triaxial Halo q=c/a: vertical-to-planar axis ratio 2. There is a preference of prolate (1:1:2) over oblate (2:2:1) Oblate 3. Spin parameter Λ = JE^½/GM^5/2 Prolate (Preferred) = 0.03 – 0.04 4. Angular momentum J is oriented along the short axis in general ΛCDM MODEL : PROBLEMS ON GALACTIC SCALE Core/Cusp Issue Missing Satellite Problem Angular Momentum Catastrophe DM BULGE DISK DISK DM ρ Predicted DISK SATELLITES Observed r (kpc) POSSIBLE REMEDY • Inclusion of Feedback: Gas accretion, cooling, Star Formation and Feedback (supernovae/AGN) • Gas Accretion • Gas Cooling Star Formation • into DM halo • Disk Formation Supernovae • Feedback POSSIBLE ALTERNATIVES • Warm Dark Matter (WDM) • Modified Newtonian Dynamics (MOND) NO CONSENSUS REACHED! DM Halos from HI rotation curve & scale height data DM HALO SHAPES: WHY BOTHER? 1. Galaxy Formation & Evolution Halo merger with no angular momentum Prolate Halo Halo merger with angular momentum Oblate Halo Moore et al. 2001 Hierarchical build-up of Dark Matter Halos in a LCDM universe: Mergers DM HALO SHAPES: WHY BOTHER? Galaxy Formation & Evolution…(continued) Vera Ciro et al. 2011 Hierarchical build-up of Dark Matter Halos in a LCDM universe: Accretion DM HALO SHAPES: WHY BOTHER? 2. Astroparticle Physics Strong self-scattering produces flatter central density profile DM HALO SHAPES: WHY BOTHER? 3. Disk Structure & Dynamics DISK Galactic Warp A prolate halo sustains a galactic warp Ideta et al. 2000 WHY HI? Stars HI Spin Flip transition from Ortho to Para state produces 21 cm line HI extends beyond 3-4 times the stellar disk ROTATION CURVE CONSTRAINT ψ total =ψ Disk +ψ DM ∴ψ DM =ψ total −ψ Disk From modeling disk luminosity profiles etc ∂ψ v2 total = rot Traditional Method ∂R R V ) R ( Expected curve for visible disk ∂ψ But total = ? ∂z R Observed Rotation Curve Cannot determine the DM halo uniquely! THE HI SCALE HEIGHT CONSTRAINT ∂ψ 1 dρ total =< v2 > ∂z z ρ dz Sensitive to the vertical-to-planar axis Observed HI scale height Curve ratio, and hence the shape of the halo! OUR STRATEGY V ) R ( Expected curve for visible disk R Observed Rotation Curve Observed HI scale height Curve Global Constraint on ∂ψ constraint on ∂ψ total total halo enclosed mass ∂R ∂z flattening DM HALO SHAPE & HI THICKNESS Observed rotation curve - total DM halo mass c c c a a a h h h Prolate (c/a = q > 1) Spherical (c/a = q = 1) Oblate (c/a = q < 1) 3 ρDM = M/V = M/4ПqR As q , ρDM , h Observed HI thickness can act as a diagnostic for halo shape! OUR CHOSEN DM HALO PROFILE Core density Density index ρ ρ (R, z) = 0 DM p z 2 R2 + q2 1 + 2 Rc Axis-ratio Core Radius De Zeeuw & Pfenniger 1988 DUAL CONSTRAINTS: 3D GRID 1. Apply rotation curve constraint q p = 1, 1.5, 2 {ρ0 , Rc, q} 50,000 grid points to be scanned! Rc ρ 0 Fit to the observed rotation curve 2. Apply HI scaleheight constraint q {ρ0 , Rc, q} 100 grid points to scan Rc Fit to the observed HI scaleheight data ρ0 OUR THEORETICAL MODEL Vertical hydrostatic equilibrium (i = stars, HI,H 2) 2 < (vz) > ∂ρ ∂ψ i i = − total (1) ρi ∂z ∂z Joint Poisson equation for disk + DM halo 2 1 ∂ ∂ψ total ∂ ψ total R + = 4πG(ρs + ρHI + ρH + ρDM ) observations (2) R ∂R ∂R ∂z 2 2 Eliminating ψtotal between (1) & (2), ∂2ρ ρ 1 ∂ρ 2 1 ∂ i = i −4πG ρ + ρ + ρ + ρ + i − v2 2 2 []()s HI H2 DM ()rot ∂z < (vz )i > ρi ∂z R ∂R (3) SOLUTION OF THE EQUATIONS At each R, 2 ∂ 2 ρ ρ 1 ∂ρ s = s − 4πG ρ + ρ + ρ + ρ + s 2 2 [ ()s HI H 2 DM ] ∂z < (vz )i > ρs ∂z ρHI (z; ρ DM (ρ ,0 Rc ,q, p)) → HI vertical thickness (theoretica l) 2 ∂ 2 ρ ρ 1 ∂ρ HI = HI − 4πG ρ + ρ + ρ + ρ + HI 2 2 [ ()s HI H 2 DM ] ∂z < (vz )i > ρHI ∂z 2 2 ∂ ρH ρH 1 ∂ρH 2 2 2 = []− 4πG()ρs + ρHI + ρH + ρDM + 2 2 2 ρ ∂z ∂z < (vz )i > H 2 Applications & Results RESULTS: ANDROMEDA (M31) Surface density of the disk components and Dark ρ0 Matter vs R ρ(R, z) = p z 2 R2 + q2 1+ 2 R c q= 0.4 (oblate) Rc ~ 4 RD DM dominates beyond 3 RD Banerjee & Jog 2008, ApJ, 685, 254 RESULTS: UGC 7321* Surface density of the disk components and Dark Matter vs ρ0 R ρ(R, z) = p z 2 R2 + q2 1+ 2 R c q = 1 Rc ~ RD (compact) DM dominates just beyond RD Banerjee, Matthews & Jog 2010, NewA, 15, 89 RESULTS: THE GALAXY Best-fit vs observed HI thickness ρ0 ρ(R, z) = p z 2 R2 + q2 1+ 2 R c q= 1 (spherical) p = 2 But total DM halo mass small! Narayan et al. 2005 RESULTS: THE GALAXY DM halo isodensity contours q (R) = 0.02R + 0.003R^2 A progressively more prolate (i.e q increases with R) DM halo! Banerjee & Jog 2011, ApJL, 732, L8 SUMMARY 1. We use the joint constraint of the HI rotation curve and the HI vertical scale height data to track the DM density profiles of nearby edge-on galaxies. 2. The DM halo shape can vary from oblate, spherical to prolate and can also vary with radius. 3. The DM halo is compact in case of the LSB superthin galaxy whereas extended in case of the HSB galaxies. et cetera…. Effect of the DM halos on Disc Structure & Dynamics WHY ARE SOME GALAXIES SUPERTHIN? Banerjee & Jog 2013, MNRAS, 431, 582 THE SLOW BAR IN NGC 3741 (Debattista & Sellwood 1998, 2000) 3 Fd ~ ρ/v rel (Chandrasekhar 1943) Banerjee, Patra, Chengalur & Begum 2013, MNRAS, 434, 1257 BROAD AREAS OF DM RESEARCH 1. Dark Matter in Galaxy Formation and Evolution (Simulations) 2. Tracking the Dark Matter density profiles in clusters, groups and galaxies (Observations) 3. Predicting constituent particles for Dark Matter (Astroparticle Physics) 4. Dark Matter detection experiments .