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Gaia ITNG2013 School, Tenerife
Ken Freeman, Lecture 2: the thin disk
September 2013
The Thick Disk
Thick disk
Most spirals (including our Galaxy) have a second thicker disk component
The thick disk and halo of NGC 891 (Mouhcine et al 2010): thick disk has
scale height ~ 1.4 kpc and scalelength 4.8 kpc, roughly like our Galaxy.
The thin and thick disks near the sun
Thick disks are very common in disk galaxies. In large galaxies like
the MW, the thick disk is about 10% of the luminosity of the thin disk.
The thick disk near the sun
was identified in 1983 from star
counts by Gilmore & Reid
towards the S. Galactic pole.
Two superimposed exponential distributions were seen :
one with scale height ~ 300 pc
and the other with ~ 1000 pc.
As expected from the different
scale heights, the vertical
velocity dispersion of the thick
disk is larger (~ 40 km/s) than
the dispersion of the old thin
disk (~ 20 km/s)
Gilmore & Reid 1983
rapidly
rotating
disk &
thick disk
slowly
rotating
halo
|Zmax| < 2 kpc
Rotational velocity of nearby stars relative to the sun vs [m/H]
(V = -232 km/s corresponds to zero angular momentum)
(Carney et al 1990)
Selecting thin and thick disk stars kinematically.
Although the thin and thick disks are dynamically
different, this approach has obvious problems
Nissen 2003
Further work indicated that
• the thin disk has a large age range (long known) and an
abundance range [Fe/H] from about -0.5 to +0.5
• the thick disk stars are all old (> 10 Gyr) and have abundances
between about -0.3 to -1.2, with a metal-weak tail extending
down to about -2.0.
• the thick disk stars form an -enhanced sequence in the [ /Fe] vs
[Fe/H]. Because of operational difficulties in assigning individual stars
kinematically to the thin or thick stars, the assignment is now usually
made according to the location in the [ /Fe] - [Fe/H] plane.
(-enhancement indicates that the chemical evolution of the gas from
which these stars formed was quick, driven mainly by the -producing
core collapse SNII. The time-scale was short compared to the ~ Gyr
timescale for the Fe-producing SNIa)
thick disk
what is this ?
thin disk
[/Fe] vs [Fe/H] for thin and thick disks near the sun
The thick and thin disks appear chemically distinct.
Haywood et al argue that thick disk is more extended now in age and metallicity
Is there an age spread and age-metallicity relation within the thick disk ?
Haywood et al 2013
Our Galaxy has a significant thick disk
• its scaleheight is about 1000 pc, compared to 300 pc for the
thin disk and its velocity dispersion is about 40 km/s compared
to 20 km/s for the thin disk near the sun
• its surface brightness is about 10% of the thin disk’s.
• it rotates almost as rapidly as the thin disk
• its stars are older than 10 Gyr, and are
• alpha-enriched so its star formation was rapid
From its kinematics and chemical properties, the thick disk
appears to be a discrete component, distinct from the thin disk.
(Some disagreement about this)
The old thick disk is a very significant component
for studying Galaxy formation,
because it presents a
kinematically and chemically recognizable
relic of the early Galactic disk.
Disk Kinematics
17000 Segue stars
Velocity dispersion components
decrease with increasing [ / Fe],
from thin disk on L to thick disk on R.
For the thin disk near sun,
 = (40, 25, 20) km/s
For the thick disk
 = (60, 40, 40) km/s
0.0
Lee et al 2011
0.1
0.2
0.3
0.4
Lag as function of [Fe/H]: thin and thick disk separated
by [/Fe]. Note the opposite trends with [Fe/H].
The metal-richer thin disk stars have a larger lag (i.e. lower angular
momentum and therefore smaller guiding center radii).
Lee et al 2011
Considering the changing lag in terms of an equilibrium disk, the
asymmetric drift in an equilibrium system depends on the
R-component of the velocity dispersion and the term in [ ] below
For disk stars the last term in [ ] is not free - it is a fixed ratio,
depending on the Oort constants.
Usually there is a positive relation between lag and velocity dispersion,
driven by the velocity dispersion. The term in [ ] does not change much
from one sample of thin disk stars to another.
From the SEGUE data, the U, V dispersion components of the thin disk
don’t change much with abundance, so the increase in lag with increasing
[Fe/H] must be due mainly to the first [ ] term via the radial density gradient.
The density gradient of the more metal rich thin disk stars must be steeper.
Lag in mean rotation vs |(height above the plane)|
Lee et al 2011
How old are the oldest nearby thin disk stars ?
i.e. when did the thin disk start to form ?
About 8-10 Gyr, from
• the age of stars at the change of kinematics from thin disk to
thick disk (~ 10 Gyr : Edvardsson et al 1993)
• the oldest subgiants in the nearby disk (~ 8 Gyr : Sandage
et al 2003) and the ages of oldest individual disk stars
(9.7 ± 0.6 Gyr : Liu & Chaboyer 2000:)
• the white dwarf luminosity function (~ 8 Gyr : e.g. Leggett et al
1998)
old disk
Velocity dispersions
of nearby F stars
thick
disk
appears at
age ~ 10 Gyr
Freeman 1991; Edvardsson et al 1993; Quillen & Garnett 2000
Hipparcos stars with accurate parallaxes, plus CMD for
M67 (age 4 Gyr) and NGC 6791 (age 8 Gyr). Subgiants in
NGC 6791 are at the faint limit of the field subgiants.
Sandage et al 2003
White Dwarf Luminosity Function (Leggett et al 1998)
Curves show expected WDLF from cooling theory for
disk ages 7,8,9 Gyr
9
7
Leggett et al 1998
Disk Heating
(the secular increase in stellar velocity
dispersion with time through
interaction of disk stars with spiral
waves, giant molecular clouds … )
Solar neighborhood kinematics:
Several possible mechanisms for heating disk stars: eg
transient spiral arms,
GMC scattering
accretion of satellites
radial migration from inner Galaxy can also contribute
Expect heating by spiral arm/ GMC scattering to saturate after
a few Gyr, as the stars spend more time away from the galactic
plane
What do the observations show ?
What is the observed form of the heating with time ?
The facts are not yet clear ...
• One view is that stellar velocity dispersion  ~ t 0.2-0.5
eg Wielen 1977, Dehnen & Binney 1998, Binney et al 2000.
velocity
dispersion
(km/s)
W is in the
vertical (z)
direction
total
W = 0.4total
stellar age
(McCormick dwarfs, CaII emission ages)
Wielen 1977
• Another view is that heating occurs for the first ~ 2 Gyr,
then saturates.
Edvardsson et al (1993) measured accurate individual
velocities and ages for ~ 200 subgiants near the sun.
Edvardsson et al data indicate heating for the first ~ 2 Gyr,
with no significant subsequent heating. Disk heating in
the solar neighborhood appears to saturate when z ~ 20 km/s.
old disk
Velocity dispersions
of nearby F stars
thick
disk
appears at
age ~ 10 Gyr
Disk heating saturates at 2-3 Gyr
Freeman 1991; Edvardsson et al 1993; Quillen & Garnett 2000
W
Soubiran et al (2008) agree, using distant clump giants
and isochrone ages
age (Holmberg 08)
The age-velocity dispersion relation is still not observationally secure.
Measuring accurate stellar ages is difficult. (These are two independent
sets of isochrone ages: one from high resolution spectroscopic parameters
and one using Hipparcos parallaxes and photometric temperatures and
[Fe/H]. )
s = sqrt (U2 + V2 + W2 )
Age-velocity relation for GCS stars
Casagrande et al 2011
AVR for our subgiant sample, drawn from the GCS
The GCS : magnitude-limited and kinematically unbiased sample of
13,500 FGK HD-stars, with Strömgren photometry and accurate (< 1
km/s) radial velocities. Most stars have Mv between 0 and +7.
GCS provides estimates of Te, MV, [Fe/H]: we used them to select
the subgiants. Kinematics are not used in selection.
Our data: echelle spectra from about 420 to 680 nm, resolution
25,000, SN ~ 50 per resolution element. Derive spectroscopic
log g, Te, [M/H] (will soon have detailed abundances for many
elements) and isochrone ages via direct and Bayesian techniques.
Removed some double-lined binaries.
The age-velocity relation: old disk has
~ constant W = 24 km s-1 for age = 4 to 9 Gyr
For age > 10 Gyr, thick disk has W = 37 km s-1
Wylie de Boer and KCF 2013
Summary from the GCS subgiants
The old thin disk is consistent with a roughly constant
W = 24 km s-1 for age = 4 to 9 Gyr
The heating appears to saturates rather than continuing to
rise like
W ~ t 0.2-0.5
For the older (thick disk stars), W = 37 km s-1
Need to resolve this issue
We need to know whether continuing internal secular
dynamical heating is important for the evolution of the disk:
it provides a baseline for understanding the dynamical evolution
of the disk, including the
effect on the disk of interactions with subhalos
Age uncertainties are still a big problem (see Soderblom (Ann
Rev 2010). Hope that accurate distances from Gaia and
asteroseismology ages will help to improve stellar ages.
The total density and surface density of the disk near the sun
This is called the Oort limit (see Oort 1960 for a more recent
reference).
The idea is to use the vertical density distribution (z) and vertical
velocity distribution f(W) of a tracer sample of stars to derive
dynamically the total (luminous + dark) density and surface density of
the disk, e.g. via Jeans equation. Is there more matter in the disk that
we can account for from census of visible objects ?
The tracer sample must be in equilibrium so the stars need to be older
than a few Gyr. The last few estimates have used K dwarfs and K
giants - probably OK but they do include stars of all ages, some of
which may not yet be phase-mixed.
Data so far is for the solar neighborhood, but Gaia will enable
estimates of the disk density and surface density away from the sun.
Kuijken & Gilmore (1989, 1991)
For a flat rotation curve and at small z, the Jeans equation +
Poisson’s equation are
The density of matter near the sun is about 0.10 M pc-3, all of
which can be accounted for.
The surface density for |z| < 1.1 kpc is 71 ± 6 M pc-3, of which
about
48 ± 9 M pc-3 is due to the stellar component and the rest is
probably due to the dark halo.
Zhang et al (2013) - SEGUE K dwarfs
Jeans analysis: results are consistent with Kuijken & Gilmore.
They find the surface density for |z| < 1.0 kpc is 67 ± 6 M pc-2,
of which the stars provide 42 ± 5 M pc-2 and the cold gas
provides about 13 M pc-2. The rest comes from the dark halo.
The halo density near the sun is about 0.0065 M pc-3.
The Chemical Evolution of the Disk
The abundance gradient in the disk
(eg galactic cepheids: Luck & Lambert 2011)
Gradient is about -0.06 dex kpc -1
Age Metallicity
Relation near sun
Haywood 2008
Note the large
spread in abundance
for the thin disk stars
with 3 < age < 10 Gyr.
Radial migration ?
The mean abundance
of the oldest thin disk
stars is about -0.2
Gently declining AMR
with spread of about 0.8
dex in [M/H] for 3 < age
< 10 Gyr (scatter includes
the [M/H] external error of
~ 0.07)
Wylie de Boer & KCF 2012 (GCS subgiants)
The [/Fe] - [Fe/H] distribution for giants in inner and
outer Galaxy and near sun
In the inner Galaxy, most stars are in the -enhanced sequence
In the outer Galaxy, few stars are in this sequence
Suggests thick disk does not extend much beyond the solar radius
Bensby et al 2011
The abundance gradient in the outer Galaxy from clusters and
giants - gradient flattens at [Fe/H] ~ -0.4 for RGC > 15 kpc
No significant dependence of gradient on cluster age, though
gradient for the clusters older that 2.5 Gyr is a bit steeper than
for the cepheids. Consistent with inside-out disk formation.
The -enhancement of outer clusters similar to that for outer
stars (i.e. like thin disk sequence).
Yong et al 2012
NGC 300: a pure disk galaxy
Diversion to radial migration (Sellwood & Binney 2002)
Stars in disk galaxies can migrate in radius under the torque of a passing
transient spiral wave. Stars moving at similar angular velocity to the spiral
are flipped from one near-circular orbit to another: inwards or outwards.
The spiral wave must be transient, not steady - otherwise the stars conserve
their stellar Jacobi integrals, and can only move along a line in the
Lindblad (E - Lz ) diagram. (The Jacobi integral is EJ = E -  Lz )
So far, radial migration is a theoretical concept: we do not know how
important it is in reality. It could move metal-rich stars from the inner
galaxy out to the outer galaxy, and invert the abundance gradient.
z
constant EJ
break
Simulation of star formation in a disk galaxy, starting with gas settling in a dark
halo. See how stars are radially redistributed via spiral arm interaction into outer
(break) region of truncated disk. Stars that form within R = 10 kpc end up at
R = 10-14 kpc, but can also end up at R < 10 kpc. The stars are affected by
spiral waves that have a similar angular velocity to the stars themselves.
Roskar et al (2008)
Vlajic et al 2008
Reversal of
abundance
gradient in
NGC 300
Roskar et al 2008
NGC 300
Is this reversal related
to the radial migration
phenomenon ?
Is it, and the lack of
truncation of the disk,
due to strong radial
mixing of stars from
the inner disk ?
Star Formation and the Galactic Gas Supply
in Disk Galaxies
extended gas envelopes
gas depletion times
need for continuing gas supply
radial gas flows
formation of pure disk galaxies
Extended HI envelopes of disk galaxies are common
e.g. NGC 2903 Irwin et al (2009)
Outer contour 3.1017 cm-2
Vc = 190 km s-1
M83 outer HI (Bigiel et al 2010a)
Some star formation, but depletion
time ~ 100 Gyr in outer regions:
outer HI is available as reservoir
for star formation in inner regions.
HI
UV, HI
M83 outer HI Bigiel et al 2010a
Long HI depletion time in outer disk
Entraining of hot halo material by galactic fountain: SN-driven accretion
NGC 891
Much evidence now for hot halos of
gas around spirals, from COS
absorption spectra of QSOs with
sightlines through galaxies.
Fraternali et al (2001 ff) : very deep
HI observations found halo HI in
NGC 2403, 891, 4559, 6946 lagging
rotation of the disk.
In NGC 891, halo HI is detected to
z = 22 kpc from the galactic plane.
Lag in rotation relative to disk
suggests that fountain gas loses
angular momentum to the hot halo.
Binney, Fraternali, Marinacci et al (2006 ff) propose that SN-driven
fountain gas entrains hot halo material which returns to the disk.
Star formation sustains itself from the hot halo, with accretion rate
~ 2 M yr-1 in the Milky Way. (Deposition rate is smaller than the
overall rate of interchange of mass between disk and halo).
Cool clouds are ejected from the disk into halo : Kelvin-Helmholtz
instability strips gas from the clouds, and coronal gas condenses in
their wake and returns to the disk. Fountain gas loses angular
momentum to the halo and spins up the halo, which still lags the cold
disk by ~ 100 km s-1.
Radial Flows and chemical evolution
Expect slow (~ 1 km/s) radial inflow in disk as consequence of infall of matter with angular
momentum < that of local circular velocity (eg Lacey & Fall 1985). Could also be driven by
bar, spirals, viscosity. Not possible to detect observationally (Wong et al 2004: NGC 5055;
Elson et al 2011: NGC 2915): intrinsic asymmetries and warps in HI disks mask radial flows
< 5-10 km/s.
Spitoni & Matteucci (2011) looked at chemical
evolution of disk with inflow. Goal is to reproduce
an exponential stellar disk and this observed
abundance gradient in the gas. Succeed with infall
velocity increasing with radius and radially
dependent infall rate decay time (~ 8 Gyr at sun).
Not unique: other ways to get there without radial
flow.
Related study by Schoenrich & Binney (2009)
invoked radial gas flow and radial stellar
migration and stellar heating prescription.
Reproduced abundance gradient, solar n’hood
stellar MDF, bimodal alpha-Fe relation from
migration rather than SFH,
(Black points are mean of HII & PN)
Starburst- and AGN-driven winds
Metal ejection from star-forming disk, enriches halo, returns gas to disk (maybe with extra
entrained gas from halo). Believed to be essential part of understanding the massmetallicity relation enrichment of IGM …
Recent observational work on winds driven by starbursts and AGNs at low-z (Sharp &
Bland-Hawthorn 2010). See large-scale wind cone of enriched material with velocities of
100-200 km/s, accelerating to increasing heights above plane, originating from the region of
active star formation. The material seen in the winds is not the winds themselves which are
believed to be hot - we see the cooler material that is entrained in the wind.
M82 wind: red is H
From Veilleux et al 2005
The difficulty of forming large disk galaxies with small bulges
(recall Abadi et al 2003) led to current ideas on importance of
suppressing early star formation, removing baryons from forming
galaxy via massive winds and returning them slowly (Binney
Gerhard Silk 2001, Governato, Gibson ….)
UGC7321 Matthews et al (1999)
The mass loss avoids loss of baryonic angular momentum to the
assembling lumpy DM halo which leads to disks that are too small
and violate the TF law. It also suppresses the steep DM cusps which
are ubiquitous in CDM simulations but are not observed in galaxies.
In the current generation of simulations, galaxies start with
more low-J material than they end up with. The surplus is
ejected as wind. The halo absorbs some of the angular
momentum and expands. Disk forms later from higher-J
material which falls in: this suppresses the formation of large
bulges which always occurred in earlier simulations (e.g. Abadi
et al 2003).
How much of this is true - what are the details ? Simulations
are now showing these effects (eg Brook et al 2011) in context
of earlier discussion of winds, hot halo.
Brook et al (2011) on the formation of bulgeless galaxies. High resolution
cosmological SPH simulations, enough resolution to resolve star forming
regions. Adopt a high threshold density for SF: increases energy released
into gas affected by SN feedback.
In summary
• low-J material accreted and rapidly expelled early. Later
accreted material has higher-J and forms disk
• reservoir of high-J material exists beyond star forming
region
• outflows occur perpendicular to disk.
• Material that builds disk is accreted from outer regions
near the galactic plane
• mergers which cause gas to lose angular momentum trigger
starbursts which expel much of the low-J gas. (May also
expel gas which has lost angular momentum through secular
processes)
Loss of low-J material suppresses bulge formation
gas blown out
HI
Angular momentum distributions of gas and stars within rvir at z = 0
Blown-out gas has low-J
Brook et al 2011
Simulation:
B-band surface brightness
and HI contours (1019 to
1022 cm-2) at z ~ 1.2.
Extended HI relative to
star forming region.
mag arcsec-2
Brook et al 2011
Maccio et al 2012 show how the heating of the DM cusp via the
outflow can erase the central cusp in the DM distribution, as many
have suggested.
Low feedback
High feedback
The angular momentum content of disks (the M-J relation) is a
critical constraint on formation mechanism (eg Fall 1983,
Romanowsky & Fall 2012).
Angular momentum per
unit mass vs mass
J ~ M 0.6 where J is the
specific angular momentum
i.e. the angular momentum per
unit mass. Where does this
scaling relation come from ?
NGC 2915 Meurer et al 1996
MB = -16
Vc = 80 km/s
Abundance Z ~ 0.4 Z in outer
disk HII regions (Werk et al
2010)
NGC 5055 Battaglia et al (2006) weak warp, weakly
lopsided: inner HI dominated by stellar disk, outer HI by DM.
Some star formation in outer HI. Vc = 206 km/s.
How do the baryons get into the galaxies ?
Before about 2000, gas was believed to fall into the galaxies as the
halo was being built up. The gas clouds virialize and the gas is
shock-heated to a temperature corresponding to its virial velocity.
T ~ V 2 : for V = 200 km/s, T ~ 2.6 x 10 6 K
This gives a hot halo of gas. Getting gas out of this hot halo into the
disk to form stars is not so easy.
Since about 2003, belief is that this is still
true for the very massive DM halos (hot
halos are seen in very massive galaxies),
but accretion in filaments of cold gas
through the hot halos is more important
for galaxies with M < 2-3. 1011 M
(Dekel et al 2009)
Paradigm for baryon acquisition
Most of the baryonic mass in
galaxies with halo masses
< 2-3. 1011 M is acquired
through filamentary cold-mode
accretion of gas that was never
shock-heated to its virial
temperature (eg Birnboim &
Dekel 2003, Keres et al 2005,
2009).
Atmospheres of hot virialized
gas develop in halos above
2-3.1011 M but cold accretion
persists (especially at z > 2)
and is the main driver of the
cosmic SFH.
Keres et al 2009
How to get the hot gas from the halo into the disk to fuel star formation
(and how to get it out of the disk into the halo)
High Velocity Clouds: (infalling HI clouds around the MW), long believed to be
gas fuel source for the disk. Their formation is not completely understood yet.
Their metallicities are ~ 0.2 Z (eg Sembach 2004)
Condensation of HVCs from hot halo via thermal instability (Maller & Bullock
2004). Difficult to make this work in linear theory - would be mostly
suppressed by buoyancy and thermal conduction (Binney et al 2009).
Simulations of non-linear perturbations (overdensities 10-20) can generate
cool clouds from hot halo if cooling time is shorter than the dynamical time.
Otherwise clouds are disrupted by Kelvin-Helmholtz (shear) and &
Rayleigh-Taylor (buoyancy) instabilities (Joung et al 2012)
Only larger clouds (~ 105 M) can survive the trip from halo to disk. Smaller
clouds lose their HI over ~ 10 kpc of travel and may become part of warm
ionized Galactic disk.
Keres & Hernquist (2009) simulations: at high z, gas is
accreted from intergalactic medium in cold filamentary
infall. At later times, densities are lower and filamentary
flows are disrupted in inner regions of massive halos.
Disrupted filaments are still able to supply cold gas to MWsized galaxies. Cooling and Rayleigh-Taylor instabilities
produce cold (< 104 K) clouds.
Again, process needs seeding with moderate overdensities
from the filamentary gas.
Interaction of hot halo gas with infalling satellites : is this a
significant source of fuel ?
Cosmological hydro simulations provide a guide: simulations (Fernandez et al
2012) of a MW-sized galaxy shows that the amount of HI present in the halo
since z = 0.3 is roughly constant, at about 108 M. The HI accretion rate on to
the disk is about 0.2 M yr -1. The satellites are losing gas (about 0.06 M yr -1)
so other sources are needed to fuel the current star formation rate.
Most of the cold gas in the halo comes from filamentary flows - much of it does
not make it directly to disk but some is able to cool and form clouds. Gas
stripped from satellites provides a fraction of the cold halo gas.
Kauffmann et al 2012 agree: from study of isolated central galaxies (SDSS),
accretion rate of gas from satellites is too small to feed the current star formation
rate in the primary galaxies. SFR in primary galaxies correlates with the amount
of gas in satellites - maybe the satellites are tracing a larger reservoir of ionized
gas, that is accreting on to the primaries.
Metals in the halos
If the halos are at least partly from gas ejected from star formation sites
in the disk, then they would also be a reservoir of metals. eg Tumlinson et
al (2011) found UV OVI absorption in 27/30 galaxies with sSFR > 10-11 yr -1
and only 4/12 passive galaxies with sSFR < 10-11 along sightlines with
projected radii up to 150 kpc.
log M* = 9.5 - 11.5
IGM median
Diversion
Red
Blue
The blue cloud / red sequence dichotomy is closely reflected in the chemical
properties of the gaseous halo out to 150 kpc. The dichotomy is seen in the
colors of galaxies: the red ones are mainly passive (little or no star formation) and
the blue ones are star forming.
Evolution is believed to be mainly from the blue cloud to the red sequence as blue
galaxies run out of gas or are quenched. But some galaxies may go the other
way: red galaxies that have acquired gas and restarted their star formation. See
NGC 5102 above.
Kauffmann et al 2003
The halo O-mass and total gas mass is comparable with that of the ISM.
In Tumlinson’s passive galaxies, the gas may have been stripped, re-accreted
or have cooled (or heated) so that the OVI is undetectable
The gaseous halo may be a basic component of star forming galaxies that is
removed or transformed when star formation is quenched (I.e. turned off).
cf the Fraternali & Binney 2008 mechanism of halo gas entrainment: star
formation drives the entrainment which then feeds the star formation.
What is mode of quenching in this picture - what stops the star formation ?
Mergers ?
Where does the warm halo oxygen come from ?
The O was likely produced by star formation in the disk and ejected into the
CGM. Only 0.3 Gyr of SF at the present rate would be enough to produce it if
it were all ejected. It could have accumulated over many Gyr, or be leftover
from early starbursts. An estimate of [O/Fe] (or other Fe-peak element)
In the gaseous halo could give some constraint on when enrichment occurred.
If the mass-metallicity relation of galaxies is associated with ejection and inflow
of metals, (eg Davé et al 2011) rather than by rate of SF (eg Tassis et al 2008),
then ejected material in lower-mass galaxies may be locked in the CGM and
may return later to affect their chemical evolution.
The ejected material may also feed the extended non-star-forming HI envelopes
seen in many isolated disk galaxies and raise the abundances of these
envelopes to their observed level (> 0.2 Z - eg Werk et al 2010, 2011). The
Fraternali-Binney circulation could be a way to feed the outer HI envelopes with
enriched material.
Diversion: Toomre Q
(Toomre 1964)
An axisymmetric disk is stable to axisymmetric perturbations if
where  is the epicyclic frequency, cs is the sound speed and
 is the surface density. A high sound speed (or velocity
dispersion) stabilises the disk. Although Q < 1 is a criterion for
largescale axisymmetric instability of the disk, it seems to be
related to the smaller scale star formation threshold in disks of
spiral galaxies (not a very secure result).
Very low star formation efficiency in outer regions of HI disks
Bigiel et al 2010b :
17 spirals
5 dwarfs
SF efficiency drops for lower
HI column density.
Depletion time ~ 100 Gyr in
outer regions.
In outer regions, SF
efficiency not strongly
correlated with local Q
Stabilized by DM ?
(cf Schaye 2008)
All gas at z = 0.5
Gas at z = 0.5 which
will form stars by z = 0
Outflowing gas
Disk is seen edge-on. Gas which feeds SF is near plane of the disk.
Outflowing gas is perpendicular to plane.
Brook et al 2011