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