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

• 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

NGC 891 NGC 628

NGC 628

NGC 891

M87

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

Cluster

Group

Abell 1689

Field

Robert’s Quartet

NGC 891 Dark Matter: A Brief History

Fritz Zwicky

Coma Cluster (Abell 1669) Estimable from the Doppler Shifts of the galaxy spectra Hints at the existence of Dark Matter! Estimable from the lumininosities of the galaxies

Vera Rubin

Observed

VROT =(GM/R)½

R

Observed Large Scale Structure (SDSS) Ansotropies in the Cosmic Microwave Background (WMAP)

Abundance of H, He, Li MATTER! ORDINARY ORDINARY

LCDM Model: Success & Failure

Millenium Simulation

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

Core/Cusp Issue Missing Satellite Problem Angular Momentum Catastrophe

DM

BULGE DISK DISK

Predicted

DISK SATELLITES

Observed

• 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

• Warm Dark Matter (WDM)

• Modified Newtonian Dynamics (MOND)

DM Halos from HI rotation curve & scale height data 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 Galaxy Formation & Evolution…(continued)

Vera Ciro et al. 2011 Hierarchical build-up of Dark Matter Halos in a LCDM universe: Accretion 2. Astroparticle Physics

Strong self-scattering produces flatter central density profile 3. Disk Structure & Dynamics

DISK

Galactic Warp

A prolate halo sustains a galactic warp

Ideta et al. 2000

Stars

HI

Spin Flip transition from Ortho to Para state produces 21 cm line

HI extends beyond 3-4 times the stellar disk

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 V ) R ( Expected curve for visible disk ∂ψ But total = ? ∂z R Observed Rotation Curve Cannot determine the DM halo uniquely!

∂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!

V 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

c c c a a a h h h

<

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

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

2 <(vz) > ∂ρ  ∂ψ  i i = − total  ρi ∂z  ∂z 

2 1 ∂  ∂ψ total  ∂ ψ total  R  + = 4πG(ρs + ρHI + ρH + ρDM ) observations R ∂R  ∂R  ∂z 2 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

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 ∂ ρ H ρ H 1  ∂ρ H  2 = 2 []− 4πG()ρ + ρ + ρ + ρ +  2  2 2 s HI H 2 DM ρ  ∂z  ∂z < (vz )i > H 2   Applications & Results

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

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

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

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

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

Banerjee & Jog 2013, MNRAS, 431, 582

(Debattista & Sellwood 1998, 2000)

Banerjee, Patra, Chengalur & Begum 2013, MNRAS, 434, 1257

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