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The Secular Evolution of Disc Galaxies and
the Origin of Exponential and Double
Exponential Surface Density Profiles
Bruce G. Elmegreen
IBM T.J. Watson Research Center
Yorktown Heights, NY USA
Disks in Galaxies, Garching, July 2016
APOD 10/9/11
(ApJ 1959)
(ApJ 1970)
(Freeman ApJ 1970)
curve: exponential disk
Compare:
mass (angular momentum)
for exponential disk and
collapsed, uniformly
rotating sphere with initial
WR2=2.80 (normalized)
points: flattened uniform
sphere (Mestel 1963)
versus normalized radius R/Rs
versus normalized ang. mom.
Cumulative
angular
momentum
distrubution
versus radius
The Mestel collapsing spheroid model gives a surface density profile that deviates
significantly from exponential beyond ~4 scale lengths (Ferguson & Clarke 01)
Weiner et al. 2001: Exponential out to 10 scale lengths
(surface photometry)
NGC 4123
Bland-Hawthorn et al. (2005):
NGC 300 outer disk profile
traced to 10 scale lengths
with star counts
photometry
star counts
Mihos +13
Northeast: up bending
(magenta)
Southwest: down
bending (green)
~8 scalelengths
M101
for M101 see also
van Dokkum +14,
for other galaxies,
see Grossi +11,
Radburn-Smith+12,
Barker +12, Hunter
+11,+13, …
Q: If the halo collapses to 4 scale lengths in a disk, then
how can we get 8 scale lengths in the stars?
A: Use a pure-gas Kennicutt-Schmidt slope of 2
SSFR = eff Sgas / tff for midplane tff
where midplane r = Sgas/ [2H] and H = s2 / [ p G Sgas ]
giving SSFR = eff ( 4/31/2 ) ( G / s ) Sgas2
= 1.7 x 10-5 (Sgas/[1 MO/pc2])2 (s/6 km s-1)-1
with an efficiency eff ~ 1%
Elmegreen 2015
KS relation for local dIrrs & outer spiral disks versus theory
Bigiel +10, red: outer parts of spirals green: dwarfs
Elmegreen & Hunter +15 blue: 20 dIrrs
Theory,1.7x10-5Sgas
2
Elmegreen 2015
Wang +14: In gas-rich galaxies, the outer
gas radial profiles are all the same when
scaled to the radius where SHI = 1 MO/pc2.
From the pure-gas KS theory above,
SSFR = 2x10-5 MO/pc2/Myr at Sgas=1 MO/pc2
Thus, Sstars ~ 0.2 MO/pc2 in a Hubble Time
which is 10-3.5 from the central Sstars,
or 8 scale lengths in stars
or 4 scale lengths in gas
So R1 ~ 4 rs in gas, or rs/R1 ~ 0.25(Zheng +15)
far-outer gas scale
length/radius at 1
MO/pc2 ~ 0.2gas rich
gas poor
Rbk moves out over time
Aumer & White 13:
Cosmological zoom-in model with rotating
halo gas aligned in various ways with the
dark matter symmetry axes
Exponential break radius, Rbk , from the
angular momentum limit with long cooling
and SF times in the outer regions.
Aumer +13b:
16 halos from 2
LCDM simulations.
gas, SF, FB, …
some isolated at z<1,
some not.
All produce
exponential disks.
Low mass
Aumer +13b:
16 halos from 2
LCDM simulations.
gas, SF, FB, …
some isolated at z<1,
some not.
All produce
exponential disks.
High mass
Aumer +13b:
Final Radial Profiles
Erwin +12
Type I: single exponential
Type II: down-bending double exponential
Type III: up-bending double exponential
see also van der Kruit 2001, and many others
Herpich +15: finds the transition from Type
III (low l) to Type I to Type II (high l).
l=0.035 for Type I
Low spin parameter collapse has the largest
redistribution of disk mass into the outer
exponential
high l
low l
Gutierrez +11: 183 barred and non-barred galaxies (Erwin +08, Pohlen +06)
Early Hubble Type:
evenly divided among
exponential types
Late Hubble Type:
mostly Type II
down-bending
up-bending
single
Herrmann +13: Dwarfs that are not Blue Compact Dwarfs (BCDs)
follow the same trend: dominated by Type II
BCDs have steep inner parts from SF and are Type III
Summary 1: Cosmological collapse models can
get exponential or piece-wise exponential mass
profiles.
Most likely it is from a combination of effects:
initial mass + angular momentum distribution,
torques, star formation law
Next… age profiles
Bakos +08: surface brightness kinks are from color gradients, not
mass, implies old stars migrate to the outer parts (Roskar +08)
Zheng +15: 700 galaxies with deep images from Pan-STARRS
All Hubble types have single exponential mass profiles, on average
surface
brightnessmass
color M/L ratio
old starsold stars
break in light no break in mass
Munoz-Mateos +13b: 2400 galaxies at 3.6 mu (Spitzer) show down-
bending exponentials on average
= exponential
= deVaucouleurs
Roediger +12:
Age measurements show U-shape
in all exponential Types:
(color gradients are more confusing,
as they mix age with metallicity
gradients)
Age profiles for Type I exponentials
Some have U-shape
(see also Yoachim +12)
Roediger +12:
Age measurements show U-shape
in all exponential Types:
(color gradients are more confusing,
as they mix age with metallicity
gradients)
Age profiles for Type II exponentials
Some don’t have U-shape
(see also Yoachim +12)
Roediger +12: U-shape age profile in all types
Even in Type III, meaning the mass profile upturns even more
than the light profile
Generally, outer disks have old stars.
Ruiz-Lara +16:
IFU CALIFA survey: also find U-shape light-weighted age profiles (blue
dots) in Types I and II.
- Constant mass-weighted age profiles (red dots) suggest early
formation of entire disk (not migration) and inside-out quenching
Type I
Type II
Watkins +16:
very deep images.
Finds smooth outer
disks that are red
with no spiral arms isolated galaxy
possible recent merger
Watkins +16:
very deep images.
Finds smooth outer
disks that are red
with no spiral arms
small companions
Watkins +16:
very deep images.
Finds smooth outer
disks that are red
with no spiral arms
Watkins +16: outer disk color B-V ~ 0.8 mag, no FUV so
SFR < 3-5x10-5 MO/pc2/Myr.
Cannot be continuous SF and disk building in the outer parts.
- How can you get radial migration with no spiral arms?
possible halo,
but unusually
bright
Summary 2: Galaxy disks tend to have old stars
in the far-outer parts.
“Inside-out” star formation makes the disk light
get bluer and younger with radius at first, but
eventually it gets redder and older, possibly from
scattered inner-disk stars.
Next… mono-age component structure
Bird +13:
Milky Way
simulation.
Mono-age
population
study:
Older stars in
the present-
day disk have
shorter and
fatter
exponential
profiles
(see also:
Sanchez-Blazquez +09
Stinson +13,
Martig +14, Minchev +15)
sum
old
young
Flaring disks
young
old
Bovy +16: MW observations (14700 red clump stars): SF forms
metals at equilibrium Z (given potential, winds, outflows), and
migration broadens the distribution.
Rosales-Ortega +12: Metallicity depends on Smass
Bresolin & Kennicutt 15:
constant metallicity
gradient in units of the
scale length
Summary 3: Mono-age populations have increasing
exponential scale length and decreasing height for
younger ages in simulations and in the Milky Way.
The first stars were a-enhanced and are currently in a
thick disk that probably formed thick (…clumpy disk)
Later stars formed in a sequence of ever-lengthening
thin disks, each of which fattens over time.
Metallicity may depend on local conditions and is not
equivalent to age
Next… environment … galaxy interactions
Erwin +12: S0 galaxies in Virgo have proportionally more Types
I and III, suggest that interactions (mergers) are important
Bars (left versus right panel) have little effect
BarredBarred and non-barred
Borlaff +14: S0 formation by mergers can make a Type III disk
Borlaff +14: S0 Type III properties agree with merger simulations
(see also Younger +07)
Rbk/hinner Rbk/houter
hin
ner/h
ou
ter
hin
ner/h
ou
ter
Athanassoula +16: gas-rich major merger forms an exponential disk
=formation times
Maltby +12, +15 say that environment (cluster vs field) does not
affect the scale length or break strength
Hout
Hin
log
Hout
Maltby +15: Type III in some S0s (15% according to Maltby +12) have
outer brightness from the bulge.
Disk fading can make an S0 from a spiral, preserving the scale length.
(see also Cooper +13)
Sandin 2015: R and I band radial
profiles for NGC 4102 showing fit to
a single exponential model with a
broad PSF from the instrument: no
Type III excess in reality
PSF from Michard ‘02
120 cm Newtonian
Head +15: ETG (S0) in Coma cluster:
Bars are important: correlate with Types II, III
Location in the cluster is not important.
Type I Type II Type III Type I Type II Type III
Fra
ctio
n
0
0.2
0.4
0.6
0.8
1
Munoz-Mateos +13: Bars and spirals are important:
Break radius for Type II is either at the OLR of a bar (red curve) or
OLR of a spiral outside a bar (whose inner 4:1 resonance is at bar CR)
(see also Pohlen & Trujillo 2006, Erwin +08)
Rb
k/R
ba
r
Laine +14: Bars and spirals are important94% of Type II breaks are associated with a feature:
48% are in ETG with outer ring/pseudoring; 8% are with a lens (=OLR for bar)
if no outer ring, then breaks are at 2x radius of an inner ring,
(which is the factor of radii for outer to inner ring resonances)
14% are in LTG with an end to strong SF and 24% are at an end to spiral arms
30% of Type III breaks are associated with inner/outer lenses or outer rings
Summary 4: Bars, spirals, and interactions, are often
associated with exponential profiles and break radii in
one way or another, with notable variations that are
not understood yet.
Mergers can end up with Type I or III exponential
disks
Next … theory
Two issues:
1. Dynamical processes move stars radially in a disk:
– bars, spirals, interactions/mergers, cloud-star
collisions (Roskar et al., Sellwood & Binney, Minchev et al.,
Martig et al., Debattista et al., D’Onghia et al., Borlaff et al., …)
2. The new star positions have an exponential profile
– why ???
Hohl 1971
initially uniform disk
forms bar,
forms exponential profile
Clump scattering makes an
exponential disk
Bournaud, Elmegreen & Elmegreen 07
Struck & Elmegreen ‘16:
3D simulations of star-clump scattering in dwarfs
15,596 particles70 clumps of various massesA vertical force proportional to zMATLAB orbit integrations
(see also Elmegreen & Struck 2013)
5 Myr
100 Myr
1.5 Gyr
3 Gyr
Scattering by ISM holes works too
Struck & Elmegreen ‘16
2.5 Gyr
Struck & Elmegreen ‘16
Two nested exponentials: a long new one is added to a shorter
old one: Because scattering is weaker for the hotter population,
the mono-age populations evolve somewhat independently.
Consider the “Galton Box”
1D scattering:
probability to the left = q
probability to the right = p
all particles launch at Position = 30
A Galactic Galton Box in 1D (Elmegreen & Struck 2016)
1D scattering:
probability to the left = q
probability to the right = p
all particles launch at Position = 30
1D scattering with reflecting barrier
leftward bias: p<0.5
all particles launch at Position = 30
3000 scatterings per particle
scale length = 1/ ln(q/p)
A Galactic Galton Box in 1D (Elmegreen & Struck 2016)
1D: The exponential appears with increasing number of scatters
p=0.45
Two Dimensions: scatter with inward bias forms an exponential.
No reflecting barrier needed in 2D. Rs=0.5l/(q-p)
Scattering model in 2D,
with b=0.1 bias distribution
2D: Even a single particle, scattering more and more in
a disk with an inward bias, builds up an exponential pdf
3D scattering experiments (particle/cloud
or particle/hole) automatically have an
inward bias.
Struck & Elmegreen (2016)
Why an inward bias?
An initially circular orbit has a maximum angular
momentum per unit energy.
A star preserves energy when it scatters off a
massive object, but it changes angular momentum.
The angular momentum can only go down.
Summary:
• Exponential profiles can result from collapse of a gaseous halo• including some angular momentum redistribution, star formation, migration
• breaks may indicate l (Type II I III at decreasing l)
• Outer disks tend to have old stars
• migration, initial formation, bulge/halo, … +minor mergers …
• true for all types: mass profile not always a single exponential
• Mono-age populations in simulations and the Milky Way show
increasing scale length and decreasing thickness for younger
stars, and always a flare
• OLRs for bars and spirals correlate with breaks, but the effect of
environment is unclear
• Stellar migrations basically understood, exponential shape is not
• possible (likely) consequence of stellar scattering
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