/sym?Omega ASTR 553 5 : SPIRAL GALAXIES (Whittle)

Whittle : EXTRAGALACTIC ASTRONOMY

1 : Preliminaries	6 : Dynamics I	11 : Star Formation	16 : Cosmology
2 : Morphology	7 : Ellipticals	12 : Interactions	17 : Structure Growth
3 : Surveys	8 : Dynamics II	13 : Groups & Clusters	18 : Galaxy Formation
4 : Lum. Functions	9 : Gas & Dust	14 : Nuclei & BHs	19 : Reionization & IGM
5 : Spirals	10 : Populations	15 : AGNs & Quasars	20 : Dark Matter

5. SPIRAL GALAXIES

(1) Introduction

(a) Spiral Galaxies are Complex Systems

Disk galaxies appear to be more complex than ellipticals

Wide range in morphological appearance :
Wide range in stellar populations :
Wide range in stellar dynamics :
significant ISM :

(b) Review of Basic Components

Disks :
Bulge :
Bar :
Nucleus :
Stellar Halo :
Dark Halo :

(2) 3-D Shapes

(a) Disks

Distribution of (projected) b/a : [ images ]
Interpretation :
- randomly oriented thin circular disks give N(b/a) = const
- drop at low b/a due to bulge
- minimum for bulgeless Sdm : b/a ~ 0.05 - 0.1
- drop at high b/a ~ 0.8 caused by non-circular disks
Warps :
- starlight almost always flat (if undisturbed)
- however, HI is often warped (either visibly or kinematically inferred)
- 180 degree symmetry : "integral sign", with warp starting between R₂₅ and R_H
- 75% of warped galaxies have no significant companion
- origin poorly understood (see B&T § 6.6) :
  self-sustaining bending modes dont seem viable
  probably response to halo potential misaligned with disk
  example of warp : NGC 4013

(b) Bulges

probably similar to low-luminosity ellipticals
0 < < 0.7
~ oblate spheroids, flattened by rotation
~ 25% have very boxy isophotes
"peanut" (double lobed) shape (unshelled !)
however, this may also be associated with presence of a bar

(c) Bars

axis ratios plane range from 2.5 to 5.
isophote twists suggest nested bars common : bars within bars
are probably flat, since they aren't visible in edge-on spirals
however, "peanut" bulges may in fact be bars seen edge-on
note : theory suggests flat bars are unstable

(3) Surface Photometry

Two components : bulge and disk
Typically, use R^¼ plus exponential fits to : [ images ]

1-D elliptically-azimuthally averaged light profile
2-D image
this is better, since bulge & disk have different ellipticities

Note : it is important to fit both together, since R^¼ still contributes at large R, under the disk.
An exponential fit alone to the outer parts yields a steeper profile.

(a) Radial Profiles

(i) Bulge

(5.1)

where

R_e contains half the light
L_tot = 7.22 R_e² I_e
I(0) = 2000 I_e
R_e ~ 0.5 - 4 kpc (larger for early Hubble types)
Bulges follow the 2 & 3 parameter relations for ellipticals
eg I_e decreases for R_e increasing

(ii) Disk

(5.2)

where

equivalently : (R) = _o + 1.086 R/R_d (in terms of mag/ss)
R_d is the disk scale length, ie I(R_d) = 1/e I(0)
typically, R_d ~ 0.25 R₂₅ ~ 2 - 5 kpc
R_d > R_e always (eg MW : R_d ~ 5 kpc, R_e ~ 2.7 kpc)
L_tot = 2 R_d² I(0)
In practice, disk light falls sharply beyond R_max ~ 3 - 5 R_d
analogous relations to bulges : ie I_d decreases as R_d increases
ie larger disks have, statistically, lower surface brightness
I_B(0) ~ 21.65 +/-± 0.3 mag/ss (Freeman 1970, "Law" of ~const I(0) for all spirals)
However, low Surface Brightness (LSB) galaxies have now been discovered (**figure**)
Freeman "Law" is now thought to be largely a selection effect (**figure**)

(iii) Bulge to Disk Ratio

^¼

B/D = 3.57 (R_e/R_d)² (I_e/I_d)
or, equivalently

B/T = R_e²I_e / (R_e²I_e + 0.28 R_d²I_d )
where I_e = I(R_e) for the bulge component only
where I_d = I(R_d) for the disk component only

along the Hubble sequence, B/D decreases monotonically

Type	< B / T >	< D / B >
E	1.0	0.0
S0	0.57	0.7
Sa	0.39	1.5
Sab	0.32	2
Sb	0.24	3
Sbc	0.16	5
Sc	0.10	10
Scd	0.05	20
Sd	0.02	50

the data are presented here
Note there is considerable scatter :
some is intrinsic but much depends on fitting method

(b) Vertical Disk Structure

figure

(5.3a)

(5.3b)

recall, sech(z) = 2 / [exp(z) + exp(-z)]

z_o is the scale height of the disk, ie I(z_o) = 1/e I(0)
(see 4d(ii) below for further discussion of vertical disk structure)

(4) Disk Velocity Field

In general, self-gravitating systems are supported by both rotation and dispersion
Disks are cold (low dispersion) so V_rot ~ V_c, where V_c = ideal circular velocity
Note : V_c (& geometry) yeild M(< R) unambiguously

disk rotation is a very important probe of M(R)

(a) 2-D Velocity Fields : Spider Diagrams

line of nodes

In projected (sky) plane : s, = distance to nuc; angle from major axis
In unprojected (galaxy) plane : r, = equivalent location
For measured Doppler velocity field : V_los(s,), we have

(5.4a)

with tan = tan / cos i and r = s (1 + sin² tan²i )^½

Conversely, if we want to project V_c(r,) onto the sky, we have

(5.4b)

with tan = tan cos i and s = r (cos² + sin² cos²i )^½

Contours of V_los on the projected disk give a "spider diagram" [ images ]
Kinematic Major Axis (KMA) : line through nucleus perpendicular to velocity contours
Kinematic Minor Axis (KMI) : V_los contour at V_sys through the nucleus

There are various forms for V_los(s,) :

Circular velocity in inclined plane :
if V(r) is approximately flat (ie indep of r beyond initial rise)
solid body nuclear rise in V_c(r)
if disk is warped
Bars
oval disk (eg defined by non-axisymmetric halo)
spiral arms

Full datasets can be analysed as a set of independent rings, each with different V_c, PA, i [ images ]
Eg : here is an analysis of the circinus galaxy (Jones et al 2001) :
HI intensity, velocity and dispersion maps
inferred run of V(r), PA(r), i(r)
3-D model of warped disk

(b) V_max and the Tully-Fisher Relation

_max

Major axis optical (often H) rotation curves (**figure**)
HI 21 cm integrated (single dish) profile width, W₂₀ (**figure**)

2V_max = (W₂₀ - W_disp) / sin i

where W_disp = 3.6 _HI and _HI ~ 10 km/s = random component
and cos i = [(b/a)² - u²] / (1 - u²) where u is b/a for edge-on system (defines i)

Tully & Fisher (1977) recognised that V_max correlates with galaxy luminosity

L V_max ~ 3 - 4

As for the Faber-Jackson relation, the T-F relation stems from virial equilibrium :

V_c²

M/R and L

I(0) R²

(M/L)^-2 I(0)^-1 V_c⁴

T-F relation holds if (M/L)^-2 I(0)^-1 ~ const (roughly true)

Usually, choose longer wavelengths (eg I & H bands rather than B & V)

smaller scatter on the T-F relation
slightly steeper gradient ( larger) (**figure**)

L_1µ is less sensitive to star formation and dust
L_1µ tracks older population which dominates mass
this population has a more homogeneous M/L ratio

The T-F relation is one of the key methods of distance determination

first calibrate on galaxies with Cepheid distances (**figure**)
this yields the following relations :

(5.5)

then : V_max M m - M distance
these distances can then be used with redshifts to derive H_o
eg this figure yields H_o = 80 km/s/Mpc
(here is a simple cartoon illustrating the TF relation)

(c) Rotation Curve Shapes and Systematics

rise from zero at the nucleus
V_max peak at R_max
extended region close to flat

Many rotation curves have now been measured ( **figure**)
Some systematic trends are noticable :

(i) At Large Radius

V_max increases as L increases (T-F relation)[ images ]
R_max increases as L decreases (slower rising curves)
R_max increases as T increases (later Hubble types)
outer slope increases as L decreases (viewgraph)
drop in massive early types caused, in part, by high V_max from bulge
Galaxies in dense environments have falling V(r)
consistent with removing/disturbing some of the halo
Galaxies in dense environments have high fraction of anomalies in V(r)
asymmetries across nucleus
dips in disk region and inner peculiarities
consistent with tidal disturbance

(ii) At Small Radius

For luminous early type spirals, V(r) rises very rapidly (often unresolved)
dense bulge core (& black hole ?)
cf Milky Way rotation curve : figure
for low luminosity later type spirals, V(r) rises more slowly
slow rise often : V(r) r "solid body"
careful, however : sometimes, when V(r) drops, (r) increases
so V(r) is not V_c (ie rotation and dispersion both provide support)
in general : V(r) < V_c(r) (this is called asymmetric drift)

(d) Stellar Velocities in the Disk

faint

(i) Rotation

_los

_stars

_gas

sometimes, star rotation can be slower than gas
this is called asymmetric drift and indicates a higher stellar dispersion

In S0s, ~30% have counter-rotating gas disks [ images ]
< 10% spirals may even have two counter-rotating stellar disks (figure)

(ii) Dispersion

measurements indicate _z decreases exponentially with scale length 2R_d
this agrees with simple theory :
stellar dynamics for isothermal disk gives _z² = 2 G z_o
where is the surface mass density and z_o is the scale height
hence _z ^½ I(r)^½ exp(-R/2R_d), as found.
combining major and minor axis observations of _los yields _z _r
for NGC 488 we find ratios _z : : _r = 0.7 : 0.8 : 1.0
which is similar to the velocity ellipsoid in the solar neighborhood.
consider, now, the interdependence of _z and the vertical density distribution
for an isothermal disk (_z = const) stellar dynamics gives :
volume density (z) = (0) sech²(z/2z_o)
which nicely fits the observed light distribution (cf Eq 6.3b)
we also find for the scale height : z_o² = _z² / 8 G (0)
so we can use measured values of _z and z_o to calculate (0)
dark matter doesn't dominate in the MW disk near the sun
turning now to consider the exponential vertical law (Eq 6.3a)
this in fact fits edge on galaxies better at 2µm
for (z) = (0) exp(-|z| / z_o) stellar dynamics gives :
_z² = 4 G (0) z_o² [1 - ½ exp(-z/z_o)]
for z >> z_o we recover an isothermal distribution : _z = const
plane, z = 0, we have : _z(0) ~ _z(high) / sqrt(2)
disk plane is cooler than above by a factor sqrt(2)

Returning to compare with observations of the Milky Way :

there are several components of different z_o and _z
- gas and dust, z_o ~ 50 pc ; _z ~ 10 km/s
- young thin disk, z_o ~ 200 pc ; _z ~ 25 km/s
- old thick disk, z_o ~ 1.5 kpc ; _z ~ 50 km/s
we may view this as either
- superposition of several isothermal components
- cooler nearer the equatorial plane
the astrophysical origin of this is thought to be :
- _z increases with age
- stars born "cold" from molecular clouds
  dissipation ensures _z ~ sound speed and z_o is correspondingly small
- stars gradually "heated" by scattering off DMCs and spiral arms
or...
- heating of the disk over time by satellite passage and/or minor mergers
Here is a MW disk model : red=young stars; blue=gas; green=old stars; black=total

(5) Mass Estimates and Dark Matter Halos

V_c(r) gives important and unambiguous access to mass distributions

(a) Deriving M(r) from V_c(r)

(5.6)

where is a geometry factor 0.7 < < 1.2
Sphere : = 1.0, Flattened : ~ 0.7

For an exponential thin disk, one can show that :

(5.7)

This has peak : V_max at R_max ~ 2.2 R_d
for R > 3 R_max V_c(R) falls ~ R^-½ (Keplerian)
This figure shows V_c(R) for exp disk, point mass, and sphere [all with same M(<R_d) ]

(b) Results from Optical Rotation Curves

1960s (Burbidge's) gathered H rotation curves and assumed Keplerian fall-off beyond their data.
quote well defined galaxy "masses"
1970s & 80s (Rubin et al) went deeper : ~ flat out to ~ 2 - 3 R_d (figure)
conclude dark matter (careful : exponential disk still ~flat here)
Kent (1986) images same galaxies and derives rotation curves directly from light profile
they match the observed rotation curves !
dark matter not required; bulge + disk with normal M/L suffices

(c) Results from HI mapping

Fortunately, HI extends well beyond the optical disk
while H goes to 2-3 R_d (~0.75 R₂₅), HI often goes to > 5 R_d (~1.5 R_H)
V_rot rarely declines; still flat or rising well beyond the disk (sometimes out to 50-100kpc !)
fits to V_rot must have dark matter, especially in outer regions (eg beyond ~1% sky)
Typically, bulge + disk accounts for inner rotation curve (see above) with reasonable M/L_B ~ 3 - 5
dark matter halo needed, giving total M/L_B ~ 30
in general, 5 times more Dark Matter than mass in stars + gas
still only a lower limit since V_rot ~ const implies M(<R) R
currently, Dark Matter Halos have divergent masses
Nice example from van Albada et al (1985) :
image of NGC 3198 with HI distribution
rotation curve of NGC 3198 with disk + halo fit
abstract of paper summarizing results

(d) Dark Matter Halo Structure

obviously, (r) r^-2 at large radii (since V_rot is flat)
unfortunately, difficult to constrain the inner parts
usually, bulge & disk are made to fit inner V_rot (the "maximum" disk fit)
this still only yields a modest M/L (~ 3-5), suggesting DM not important here
clearly, the halo contribution drops at small radii, but functional form not known
simple model assumes "isothermal" sphere with a core :

(5.8)

which has the correct asymptotic behaviour for r >> a : (r) r^-2
integrating the mass profile gives a rotation curve :

(5.9)

which has : V_c = sqrt[4 G (0) a²] for r >> a
and V_c = sqrt[4/3 G (0) a²] × (r/a) for r << a
Here is a model halo with a core radius of 1 kpc : **figure**

(e) Disk-Halo Conspiracy

after a rapid rise, most rotation curves are ~flat at all radii :
--> in regions where V_c is determined by disk matter, and
--> in regions where V_c is determined by dark matter
how do these two different regions know they should have the same rotation amplitude ??
this is not currently understood, but indicates something important about galaxy formation
notice that a related puzzle also underlies the Tully-Fisher relation
V_max is set by the halo, while
M_I is set by the luminous matter

(6) Spiral and Bar Structures

(a) Spirals

(i) Spiral Classes

recall, two types (extremes) of spiral structure [image]
- Grand Design (AC 12), two strong arms (~10%)
- Flocculent (AC 1), more chaotic (~90%)
- Multiple Arm (intermediate), strong inner arms, outer ratty
(ii) Arm Prominence
Arm / Inter-arm contrast is useful
- for contrast m magnitudes (typically 1-2 in B), define A = dex(0.4 m)
- (note : arms poorly visible in azimuthally averaged radial profile)
A depends on color :
- Grand Design : A_B ~ A_I ~ large (1.5 - 8)
- Flocculent : A_B >> A_I ~ 1.0
  a plot of A_B / A_I vs A_I separates the classes well.
Clearly :
- spiral arms are bluer than the underlying (red) disk
- sprial arms are younger than the disk
- the old disk in flocculents is uniform
- the old disk in Grand design has spiral pattern
Interpretation :
- Grand design is a density wave : it involves a spiral in the underlying mass distribution
  global coherence implies global process generates structure
- Flocculent spirals are not density waves
  lack of coherence implies local process generates structure
(iii) Leading or Trailing ?
consider direction of rotation :
- arm ends point forward leading spiral
- arm ends point backwards trailing spiral
to decide : need to know which side is nearest :
- difficult, but try to identify the least obscured by dust (near side)
  arms are almost always trailing
many arms have dust lanes & HII regions on inside (concave) edge
trailing arms exert a torque on the disk : matter inwards, AM outwards
(iv) Pitch Angle
defined as the angle between the tangents of arm and circle
Most spirals have ~ const throughout disk
this is, in fact, predicted by density wave theory.
(v) The Winding Problem
if arms were "fixed" w.r.t. the disk (eg like leaves on water)
in reality : for Sa : < > ~ 5° ; for Sc : < > ~ 10°-30°
This suggests we might have two types of condition
Long lived spiral arms are not material features in the disk
they are a pattern, through which stars and gas move
these might be the grand design spirals
Short lived spiral arms can arise from temporary patches pulled out by differential rotation
the patches might arise from local disk instabilities, leading to star formation
these might be the flocculent spirals

(b) Bars

barred galaxies are common (~50%)
NGC 1300 is a nice example : **figure**
axis ratio up to 1:5
they can be strong : up to ~30% of the galaxy light
not fit by elliptical isophotes --- more rectangular
probably flat in disk plane
K (2.2µm) images can show bars within bars (inner bar ~independent)
light profile : I(R) along bar :
Early Hubble types and Grand design :
I(R) ~ const; strong bar; helps drive spiral pattern
Later Hubble types and Flocculant :
I(R) exponential [R_d(bar) ~ R_d(disk)]; weaker bar
Bars are straight rigid rotation of pattern with well defined _b
stars stay in the bar --- bars are not density waves
closed orbits in frame rotating at _b
stars move along the bar (in the rotating frame)
such orbits only occur for _b < _stars [ = V_c(r) / r ]
bars dont extend beyond co-rotation (CR)
(typically they extend out to ~80% of CR)
simulations suggest bars form (too!) easily (see Topic 8) :
they are long lived
they slow with age & lengthen (CR moves out as _b drops)
angular momentum is transferred to disk and halo stars :
bars may be important in long term AM redistribution in galaxies
bars can drive density wave in disk
gas motions important and interesting :
observationally :
star formation occurs at bar ends
dust lanes seen down leading edge of bar
velocity fields suggest strong non-circular motion
simulations :
orbits mildly self-intersecting >> weak shocks >> compression where dust lanes seen
inner gas loses AM and goes inwards
this gas may go to the nucleus (feed AGN?), or collect in disk near ILR
outer gas in bar stored in ring near bar ends (CR)
gas beyond this is stored in ring at OLR
may explain inner and outer rings seen in many barred galaxies