Vertical Structure of Disk Galaxies and
Their Dark Matter Halos
Arunima BanerjeeDepartment of Physics, IISc
Collaborators
Chanda Jog, Lynn Matthews, Elias Brinks & Ioannis Bagetakos
18 October 2011 TIFR, Mumbai 2
1. A general overview of disk galaxies
2. Our theoretical model for a disk galaxy-Gas gravity included self-consistently
3. Applications & Results
Part 1 Dark matter halo shapes from rotation curve & HI thickness data (outer galaxy)
Part 2 Effect of gas gravity on disk vertical structure(inner galaxy)
4. Summary
5. Future Research
Plan of the talk
18 October 2011 TIFR, Mumbai 3
NGC 891 – A spiral galaxy, seen edge-on
NGC 628 - a typical spiral galaxy, seen face-on
A general overview of disk galaxies
18 October 2011 TIFR, Mumbai 4
Building Blocks of a Spiral Galaxy
stars
Gas (HI + H2)
DM Halo
DM Halo
18 October 2011 TIFR, Mumbai 5
R
z
Pressure Support in the perpendicular plane
Rotation Support in the plane 0 Vrot = 220 km/s
vz(star) = 18 km/s; vz(gas) = 5-8 km/s
The Disk ( Stars + Gas )
RΔ
zΔ
301~
Rz
ΔΔ
18 October 2011 TIFR, Mumbai 6
Dark Matter HaloV
( R
)
Expected curve for visible disk
R
Observed Rotation Curve
Observed Rotation Curve remains flat with R
Hints at the presence of (unseen) gravitating matter in
the outer galaxy
DARK MATTERDARK MATTER
diskDark Matter
Disk vertical structure also hints at the presence of the dark matter !
18 October 2011 7
Our theoretical model
Vertical hydrostatic equilibrium (i = stars, HI, H2)
(1)
Joint Poisson equation for disk + DM halo
(2)
(3)
( )⎟⎠⎞
⎜⎝⎛
∂∂
−=∂∂><
zzv totali
i
iz ψρρ
2
)(4122
2
DMHHIstotaltotal G
zRR
RRρρρρπ
ψψ+++=
∂
∂+⎟
⎠
⎞⎜⎝
⎛∂
∂∂∂
Eliminating ψtotal between (1) & (2),
( )[ ] ( )22
22
2 114)( 2 rot
i
iDMHHIs
iz
ii vRRz
Gvz ∂
∂−⎟
⎠
⎞⎜⎝
⎛∂∂
++++−><
=∂
∂ ρρ
ρρρρπρρ
observations
Part 1: Known functional form (parameters to be constrained by observed vertical scale height)
Part 2: Known value from mass models (to predict vertical scale height)
18 October 2011 TIFR, Mumbai 8
( )[ ]2
22
2 14)( 2
⎟⎠
⎞⎜⎝
⎛∂∂
++++−><
=∂
∂z
Gvz
s
sDMHHIs
iz
ss ρρ
ρρρρπρρ
( )[ ]2
22
2 14)( 2
⎟⎠
⎞⎜⎝
⎛∂
∂++++−
><=
∂
∂z
Gvz
HI
HIDMHHIs
iz
HIHI ρρ
ρρρρπρρ
Solution of the equations
( )[ ]2
22
22
22
22 14)( ⎟⎟
⎠
⎞⎜⎜⎝
⎛
∂
∂++++−
><=
∂
∂
zG
vzH
HDMHHIs
iz
HH ρρ
ρρρρπρρ
At each R,
Stars
HI
H2
18 October 2011 TIFR, Mumbai 9
Part 1 Galactic Dark Matter Halos from Rotation curve and HI scale height data
Applications & Results
18 October 2011 TIFR, Mumbai 10
Galactic DM halo: Motivation
DM on galactic scales
Galaxy formation and evolution is not clearly understood (cusp/core issue; missing satellite problem)
DM halo shape
-stability of spiral arms and warps-imprints of the galaxy formation and evolution history-constituents particles of DM
18 October 2011 TIFR, Mumbai 11
Rotation Curve Constraint
DisktotalDM
DMDisktotal
ψψψψψψ−=∴
+=
Rv
Rrottotal2
=∂
∂ψ
From modeling disk luminosity profiles etc
?=∂
∂ztotalψ
V (
R )
Expected curve for visible disk
R
Observed Rotation Curve
But
Cannot determine the DM halo uniquely!
Traditional Method
18 October 2011 TIFR, Mumbai 12
The HI scale height constraint
dzdv
z ztotal ρ
ρψ 12 >=<∂
∂
Observed HI scale height CurveSensitive to the vertical-to-
planar axis ratio, and hence the shape of the halo!
18 October 2011 TIFR, Mumbai 13
DM halo shape & HI thickness
c
ca
c
a a
Spherical (c/a = q = 1) Oblate (c/a = q < 1)
ρDM = M/V = M/4ПqR3
As q , ρDM , h
Prolate (c/a = q > 1)
h h h
Mass enclosed within R from
rotation curve
DM
DM
DM
z = 0z = 0
Assumption: DM halo is spheroidal
18 October 2011 TIFR, Mumbai 14
Our StrategyV
( R
)
Expected curve for visible disk
R
Observed Rotation Curve Observed HI scale height Curve
Rtotal
∂∂ψ
ztotal
∂∂ψ
Global constraint on
enclosed mass
Constraint on halo
flattening
18 October 2011 TIFR, Mumbai 15
Our chosen DM halo profile
p
c
DM
RqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),(ρ
ρ
Core density Density index
Core Radius Axis-ratio
De Zeeuw & Pfenniger 1988
18 October 2011 TIFR, Mumbai 16
Dual Constraints: 3D Gridp = 1, 1.5, 2
{ρ0 , Rc, q}
0ρ
q
cR
{ρ0 , Rc, q}
0ρ
q
cR
1.
2.Fit to the observed rotation curve
Fit to the observed HI scaleheightdata
50,000 grid points to be scanned!
100 grid points to scan
Apply rotation curve constraint
Apply HI scaleheight constraint
18 October 2011 TIFR, Mumbai 17
Results: Andromeda (M31)
p
cRqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),( ρρ
q= 0.4 (oblate)
Banerjee & Jog 2008, ApJ, 685, 254
q = 0.4 lies at the most oblate end of the range of
halo shapes found in cosmological simulations!
Best-fit vs observed HI thickness
18 October 2011 TIFR, Mumbai 18
Results: Andromeda (M31)…
p
cRqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),( ρρ
4 RD
Surface density of the disk components and Dark Matter vs R
DM dominates beyond
~ 3 RD
Banerjee & Jog 2008, ApJ, 685, 254
18 October 2011 TIFR, Mumbai 19
Results: UGC 7321*
p
cRqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),( ρρ
q= 1 (spherical)
Banerjee, Matthews & Jog 2010, NewA, 15, 89*superthin low surface brightness galaxy
Best-fit vs observed HI thickness
18 October 2011 TIFR, Mumbai 20
Results: UGC 7321* …
p
cRqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),( ρρ
~ RD (compact)
Banerjee, Matthews & Jog 2010, NewA, 15, 89
Surface density of the disk components and Dark Matter vs R
DM dominates
just beyond
~ RD
18 October 2011 TIFR, Mumbai 21
Results: The Galaxy
p
cRqzR
zR
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛+
+
=
2
2
22
0
1
),( ρρ
= 2
= 1 (spherical)
Narayan et al. 2005
But total DM halo mass
small !
Best-fit vs observed HI thickness
18 October 2011 TIFR, Mumbai 22
Results: The Galaxy…
Banerjee & Jog 2011, ApJL, 732, L8
A progressively more prolate
(i.e q increases with R) DM
halo!
DM halo isodensity contours Best-fit vs observed HI thickness
18 October 2011 TIFR, Mumbai 23
The DM halo shape can range from being prolate to oblate, and the shape can vary with radius even within R ~ 8 RD
Future Work
What drives the DM halo shapes on galactic scales?
- cosmological merging history ?- Back effect of the baryons ?
Summary & Future Work
18 October 2011 TIFR, Mumbai 24
The superthin LSB galaxy has a dense compact halo as opposed to the HSB’s.
Future WorkDM halos in superthin dwarf LSB’s dense, compact in general?
If yes,What is the origin of the dense compact halos in the superthindwarf LSB’s and diffuse halos in HSB’s?
Is the superthin stellar disk the reflection of the dense, compact DM halo?
Summary & Future Work…
18 October 2011 TIFR, Mumbai 25
Part2 Effect of gas gravity on disk vertical structure
Applications & Results
18 October 2011 TIFR, Mumbai 26
Being a low dispersion component, gas forms a dense layer closer to the midplane & pinches the
layer of stars!
STARS vz(stars) = 18 km/s
GASSTARS
vz(gas) = 8 km/s
Pinching effect of the gas layer
18 October 2011 TIFR, Mumbai 27
z ( kpc)
ρ sta
rs(z
)
0
At a given R
Sech2 (z/zo) (Theoretical)
Sech(z/z0)
Or
Exp(z/z0)
(Observed)
Steeper density profile
density falls with z more rapidly
pinched layer thickness
The origin of the steep vertical stellar density profile in the Galactic disk
18 October 2011 TIFR, Mumbai 28
0~
( )[ ] ( )roti
iDMHHIs
iz
ii vRRz
Gvz
22
22
2 114)( 2 ∂
∂−⎟
⎠⎞
⎜⎝⎛∂∂
++++−><
=∂∂ ρ
ρρρρρπρρ
ρDM << ρs + ρHI
taken from a Mass Model
Application of our 3-component Galaxy model
Gas gravity
18 October 2011 TIFR, Mumbai 29
Results: Steepening effect of gas gravity
Banerjee & Jog 2007, ApJ, 662, 335
18 October 2011 TIFR, Mumbai 30
Comparison with Observations
3-parameter family of curves suggested by van der Kruit(1988)
)2/(2)( /2/2e
ne
nstars znzSechz ρρ −=
A higher value of n denotes a steeper vertical profile
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0
2-2/nSe
ch2/
n (nz/
2ze)
z
n=1 (Sech2)
n=2 (Sech)
n=infinity (exp)
18 October 2011 TIFR, Mumbai 31
Molecular Ring
Radial variation of ‘n’
Banerjee & Jog 2007, ApJ, 662, 335
18 October 2011 TIFR, Mumbai 32
HI scale height in dwarf galaxies
DDO 154
NGC 2366HoII
IC 2574
18 October 2011 TIFR, Mumbai 33
o Gas rich galaxies - Good model for high red-shift galaxies
o Why determine gas scale height?
-Irregular: Observationally un-amenable but crucial in calculating star-formation rates etc
o Our model of gravitationally-coupled stars and gas is ideal to study the dwarf irregulars where gas gravity is comparable with stellar gravity.
Why study dwarf irregulars?
18 October 2011 TIFR, Mumbai 34
Results
Important implications for star-formation rates in these galaxies!
HI scaleheight vs R Midplane density vsR
Banerjee, Jog, Brinks & Bagetakos 2011, MNRAS, 415, 687
18 October 2011 TIFR, Mumbai 35
Gas gravity strongly regulates the disk vertical structure
Future Work
-Imprint of Gas Gravity on the Thick Disk
- Effect of gas gravity on DM halo shapes: Prominent at higher redshifts?
Summary & Future Work