“Non-linear violent disc instability with highToomre’s Q in high-redshift clumpy disc galaxies”
MNRAS, 456, 2052 (2016)

Shigeki Inoue (Kavli IPMU, U. Tokyo)
w/ Avishai Dekel, Nir Mandelker, Daniel Ceverino,Frederic Bournaud, Joel Primack

Clumpy galaxies• Observed in the high-z universe （z > 1）
– clump clusters / chain galaxies
in the high-zwith HST～109 yr

Guo et al. (2014)

in the local universe

Elmegreen et al. (2013)• `Clumpy’ galaxies are formation stages of disc galaxies.
– `Giant clumps’ (~ 109 M at the largest)– Clumpy galaxies account for ~ 30-60 % in z=1-3• Tadaki+14, Murata+14, Livermore+15, Guo+15, Shibuya+15

Clumpy galaxies

Shibuya et al. (2015)

Clumpy fraction of galaxies• Clumpy galaxies account for ~ 30-50 % in z=1-3
 Tadaki+14, Livermore+15, Guo+15, Shibuya+15

Guo et al. (2015)

Why are they clumpy?

• It has been proposed;

 Galaxies are highly gas-rich (stream-fed) in their early formation stages.
 Cold gas discs in the galaxies are Toomre unstable (Noguchi 1998, 1999).

Clump formation is caused by ‘Toomre instability’
Stars

Gas

Inoue & Saitoh (2012)

Toomre instability• From a local and linear perturbation theory foraxisymmetric perturbations,
Velocity dispersion
or sound speed(pressure)

Epicyclic frequency(Coriolis force)

The stability condition:
Surface density(gravity)

If Q<1, the local region isgravitationally unstable,going to collapse.

Toomre instability• From a local and linear perturbation theory foraxisymmetric perturbations• But, actually Global effect may work for instability.

 Perturbations may grow non-linearly.

 Perturbations may be non-axisymmetric.

Galaxies in cosmological context may deviate
from the “idealized” situation.

Toomre analysis in cosmological sims.

•Cosmological simulations

 Ceverino et al. (2010, 2013) using ART code 10pc-order resolution with radiation pressure.

How to measure• 2-component model (Romeo & Wiegert 2011)
,.








is calculated from mean velocity fields of gas/star.
≡2+

 Young stars (age<100 Myr) are considered to be “gas “ Bulge stars are removed
 Gaussian smoothing with FWHM=1.2 kpc
 to focus onM

 A razor-thin disc model (which gives lower limits)

Cosmological simulations• V07••••••M
M
(kinematic)M yr-1

log Σgas [M pc-2]

log Σstars [M pc-2]

gasstars
log Σ [M pc-2]

σ [km s-1]

log κ [km s-1 kpc-1]

log Q

Purple Q<1: linear instability
Blue Q=1-1.8: non-linear instability
Green Q=1.8-3: dissipative instability
Yellow, Red, Black: Q>3: stable state
White: imaginary κ (Q cannot be defined)log Σgas+stars [M pc-2] log ΣSFR [M yr-1 kpc-2]

log Q2comp• Instability (Q<1) can only be seen in/around the clumps.
• Disc (inter-clump) regions seem to be stable (Q>2).
Purple Q<1: linear instability
Blue Q=1-1.8: non-linear instability
Green Q=1.8-3: dissipative instability
Yellow, Red, Black: Q>3: stable state
White: imaginary κ (Q cannot be defined)Cosmological simulations
•V08



M
M
(kinematic)M yr-1log Σgas [M pc-2]log Σstars [M pc-2]

log Q2comp• Instability (Q<1) can only be seen in/around the clumps.
• Disc (inter-clump) regions seem to be stable (Q>2).
Purple Q<1: linear instability
Blue Q=1-1.8: non-linear instability
Green Q=1.8-3: dissipative instability
Yellow, Red, Black: Q>3: stable state
White: imaginary κ (Q cannot be defined)Cosmological simulations
•V13






M
M
(kinematic)M yr-1

log Σgas [M pc-2]

log Σstars [M pc-2]

log Q2comp• Instability (Q<1) can only be seen in/around the clumps.
• Disc (inter-clump) regions seem to be stable (Q>2).
Purple Q<1: linear instability
Blue Q=1-1.8: non-linear instability
Green Q=1.8-3: dissipative instability
Yellow, Red, Black: Q>3: stable state
White: imaginary κ (Q cannot be defined)Non-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumpsNon-linear formation of clumps• Distributions of Q on proto-clumps.
 The initial masses Mclump >Clump detection scheme(Mandelker+ 2014)

We trace clumps back intime and space, and thenwe look into proto-clumps
which are detected forthe first time.

MNon-linear formation of clumps• Distributions of Q on proto-clumps.
 The initial masses Mclump >MClump detection scheme(Mandelker+ 2014)

We trace clumps back intime and space, and thenwe look into proto-clumps
which are detected forthe first time.

Significant fractions of clumps start forming with Q>1.8

How do giant clumps form?

• Non-perturbative scenarios
Gas dissipation

if gas cooling is rapid.(Elmegreen 2011)

How do giant clumps form?

• Non-perturbative scenarios
Gas dissipation

if gas cooling is rapid.(Elmegreen 2011)
Small-scale formation and growth following
Q can be <1 on small scale (e.g. Romeo et al 2010)
 Q-measurement can depend on physical scales, e.g. Larson low

 We applied the Gaussian smoothing with FWHM=1.2 kpc
A giant clump may form bymergers of small clumps.
(Behrendt et al. 2015)

How do giant clumps form?

• Non-perturbative scenarios
Gas dissipation

if gas cooling is rapid.(Elmegreen 2011)
Small-scale formation and growth following
Q can be <1 on small scale (e.g. Romeo et al 2010)
Non-axisymmetric perturbation
Rossby wave instability (Lovelace & Hohlfeld 1978) A ring structure can break up into clumps

perturbations (Griv & Gedalin 2012) unstable up to.

How do giant clumps form?

• Perturbative scenarios
Minor mergers Satellite accretion can disturb a disc.

Pre-existing clumps Clumps also disturb a disc and stimulate formation ofother clumps.

How do giant clumps form?

• Perturbative scenarios
Minor mergers

 Satellite accretion can disturb a disc.

Pre-existing clumps Clumps also disturb a disc and stimulate formation ofother clumps.

Cold stream flowing in a disc

 Streams can join a disc with slow or counter rotation.
 Slow rotation leads to low

How do giant clumps form?

• Perturbative scenarios
Minor mergers

 Satellite accretion can disturb a disc.

Pre-existing clumps Clumps also disturb a disc and stimulate formation ofother clumps.

Cold stream flowing in a disc

 Streams can join a disc with slow or counter rotation.

Compressive turbulence Compressing gas can indicate a high
 But a clump will form there(i.e. high Q)

High σ and high Q

But, stars will form

Summary• We utilized the cosmological simulations and performed theToomre analysis for high-z disc galaxies.
 Focusing on massive clumps ofM on ~1kpc scale.

• Q>2-3 in disc (inter-clump) regions,• Q<1 inside/around giant clumps.

• Formation of new clumps can start with Q>2-3.

• Clump formation is NOT NECESSARILY due tothe (standard) Toomre instability.

• Maybe induced by other mechanisms.
 minor mergers, pre-existing clumps, cold streams, etc..

最近知りたいこと• 遠方円盤銀河のクランプは、

 必ずしもトゥームレ不安定のせいというわけではなさそう。
 では、どういう物理でクランプを作るのか?

• なぜ力学不安定性の結果が違うのか?
 近傍の円盤では 渦状腕
 遠方銀河では クランプ

• しかし、両方ともトゥームレ不安定の結果とされている。
 同じ不安定性ならば、なぜ結果がちがっているのか?