BBaarrrreedd GGaallaaxxiieess

Contents

§0 Introduction: Importance of Galactic Bars §1 General Observed Properties of Barred Galaxies

§2 Dynamical Effects of Bars

§3 Dynamics of Bars

§4 Origins (Formation) of Bars

§5 Evolution of Bars

§6 High-z Bars: Cosmological Perspectives

2

§0 Introduction: Importance of Galactic Bars ( deserves one semester!)

0.1 Fundamentality and Ubiquity of bars

Disk galaxy = disk + bulge + bar

Hubble classification of galaxies

3

Bar incidence along Hubble Sequence

RC3 (B band visual morphology) (Elmegreen et al.,2004,ApJ,612,191)

Near-infrared

NGC 253

2MASS image (JHK)

4

Near-infrared (Eskridge et al., 2000,AJ,119,536)

Ohio State University (OSU) Bright Spiral Galaxy Survey (Eskridge et al. 2002, ApJS,

143, 73)

[・ BVRJHK imaging of 205 spirals (from RC3)

with 0 ≦ T ≦ 9, MB ≦ 12, D ≦ 6.5', -80° < δ < +50°

・ 6 telescopes (aperture 0.9-2.4m)]

186 galaxies with no companion, no peculiarities

Visual inspection of H band images morphological types, bar types

Comparison with optical classification

RC3 (Third Reference Catalogue of Bright Glalaxies, de Vaucouleurs et al.,1991)

D25>1’, B<15.5, Vhel<15000km/s + other interesting objects

CAG (Carnegie Atlas of Galaxies, Sandage & Bedke, 1994)

optically weak bars (SAB) tend to be classified as strongly barred (SB) in H band

5

H-band bar fraction not dependent on Hubble types

Early types: H-band bar frequency = optical bar frequency

Late types : H-band bar frequency > optical bar frequency

( probably because of dust and young stars in late types)

0.2 Effect of bars on galaxy evolution

Non-axisymmetric gravitational field redistribution of mass/angular momentum

- Trigger nuclear starbursts and AGN

6

- Secular formation of bulges

- Formation of rings

7

§1 General Observed Properties of Barred Galaxies

1.1 Stellar Components (optical observations)

1.1.1 Components of barred galaxies

Disk + Bulge + Bar + Rings (nuclear ring, inner ring, outer ring) + Lens

1.1.2 Structural parameters of bars

length, ellipticity, shape of isophotes (deviation from perfect ellipses)

tangential force (Q)

Analysis:

- eye estimate on images

- quantitative analysis (Ellipse fit)

- Not ellipse fit (Chapelon et al., 1999, AA, 345, 81)

8

◆ Elmegreen & Elmegreen (1985,ApJ,288,438)

I band surface photometry of 15 barred galaxies

luminosity profile, bar length (visual estimate)

9

◆ Martin (1995,AJ,109,2428)

Sample: 136 SAB and SB galaxies in CAG( Sandage & Bedke, 1988) Atlas (B-band)

Visual determination of bar semi-major (a) and semi-minor (b) axes

Lb(i)≡2a/D0

D0: deprojected diameter at 25 mag/arcsec2

10

◆ Regan & Elmegreen (1997,AJ,114,965)

K band photometry of 10 barred galaxies & Ellipse fit

11

7 = flat bar (half have isophotal twist in center)

3 = exponential bar (none has twist)

All bars have a maximum ellipticity at the bar end

◆ Whyte et al. (2002,MN,336,1281)

OSU sample (Ohio State University Bright Spiral Galaxy Survey)

12

1.1.3 Bar Colors

◆ Burkhead & Burgess (1973,AJ,78,606)

UBV photometry of NGC 1300(SBbc)

82inch reflector (McDonald Observatory)

major and minor (displaced from the nucleus) color profiles

bar major axis: bar redder than outside bar, bar color becoming redder to the

center.

: Q(reddening-free parameter) slightly increases toward the

center.

13

◆ Benedict(1976,AJ,81,799)

B,V photometry of N4548(SBb),N4596(SB0+),N4608(SB0)

B, B-V profiles along bar major and minor axes

N4548: bulge B-V=1.02, bar B-V=0.90, arm/disk B-V=0.82

N4596: 0.90 0.85 0.79

N4608: 0.91 0.86 0.89

bar has no internal color variation

bar is a little bluer than bulge

◆ Elmegreen & Elmegreen (1985,ApJ,288,438)

B and I photometry of 15 barred galaxies

Bar has the same color as the inter-bar regions (while spiral arms are generally

bluer than inter-arm regions)

◆ Prieto et al. (2001,AA,367,405)

UBVRI photometry of 11 disk galaxies

1) Color map qualitative idea of existing components in that galaxy.

2) Confirm each component by ellipticity and PA profiles

3) Fit the azimuthally averaged or individual profiles (i.e. profiles along major and

minor axes of the bar, for strongly barred galaxies) by those components.

Minor axis profile disk and bulge parameters

these are subtracted from major axis profile bar parameters

(Assume analytic functions for each component)

- Found bars in half of the sample.

- Half of these bars have the same color as the underlying structure,

while the other half have redder colors.

1.1.4 Rings and lenses

◆ Kormendy (1979,ApJ,227,714)

Properties and occurrence of inner rings, outer rings, lenses

Sample: 121 barred galaxies from RC2

1) SB classification, 2) BT<12.5, 3)δ >-30°, 4) not edge-on

14

Results:

- Lenses are more common in early-type galaxies, and inner rings in late-type

galaxies (Table 3).

- A significant fraction of galaxies of all types have neither a ring nor a lens

(Table3).

- Shapes of lenses and inner rings

15

inner rings are round and planar.

lenses cannot be fit with planar ellipses ( lenses are slightly triaxial, moderately

to highly flattened ellipsoids, with a typical axial ratio in plane of about 0.9 ).

- Outer rings

13 out of 121 galaxies have an outer ring

Outer rings are elongated (<b/a> = 0.76) perpendicularly to bar, and have length

2.2 ☓ bar length

- Spiral structures

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§2 Dynamical Effects of Bars

2.1 Basic Dynamics: linear theory in non-axisymmetric gravitational field

Equation of motion in rotating coordinate system

R・・

– Rθ・

2 = - ∂Φ

∂R + 2Rθ

・

Ωb + Ωb2R

Rθ・・

+ 2R・

θ・

= - 1

R ∂Φ

∂θ - 2R

・

Ωb

Gravitational potential: Φ(R,θ) = Φ0(R) + Φ1(R,θ), where |Φ1/Φ0|≪1.

Consider perturbations

R(t)=R0 + R1(t) ; θ(t)= θ0(t) + θ1(t)

1) 0-th order equation

R0θ・

02 = (

dΦ0

dR )R0

- 2R0θ・

0Ωb -Ωb2R0 R0(θ

・

0+Ωb)2 = (dΦ0

dR )R0

Introduce Ω(R)≡ R-1dΦ0

dR and Ω0≡Ω(R0)

θ・

0 =Ω0 –Ωb

θ0 = (Ω0 –Ωb)t

2) 1st order equation

R・・

1 + (d2Φ0

dR2 -Ω2)

R0R1 - 2R0θ

・

1Ω0 = - ∂Φ1

∂R |

R0

17

θ・・

1 + 2Ω0R・

1/R0 = - 1

R02 ∂Φ1

∂θ |

R0

Assume Φ1(R,θ) =Φb(R)cos(mθ)

R・・

1 + (d2Φ0

dR2 -Ω2)

R0R1 - 2R0θ

・

1Ω0 = - dΦb

dR |

R0 cos[m(Ω0 –Ωb)t]

θ・・

1 + 2Ω0R・

1/R0 = 1

R02 mΦb(R0)sin[m(Ω0 –Ωb)t]

Integration

θ・

1 = - 2Ω0R1/R0 - 1

R02(Ω0 –Ωb)

Φb(R0)cos[m(Ω0 –Ωb)t] + constant.

R・・

1 + κ02 R1 = - [

dΦb

dR +

2ΩΦb

R0(Ω –Ωb) ]

R0 cos[m(Ω0 –Ωb)t] + constant.

where κ02 ≡ (

d2Φ0

dR2 +3Ω2)

R0= (R

dΩ2

dR +4Ω2)

R0

Solution

R1 (t)= C1cos(κ0t+ψ) - [ dΦb

dR +

2ΩΦb

R0(Ω –Ωb) ]

R0 cos[m(Ω0 –Ωb)t]/Δ (2.1.1)

where Δ≡κ02 –m2(Ω0 –Ωb)2

Using θ0 instead of t,

R1 (θ0)= C1cos(κ0θ0

Ω0 –Ωb +ψ) + C2cos(mθ0) (2.1.2)

C2 ≡ - 1

Δ [

dΦb

dR +

2ΩΦb

R0(Ω –Ωb) ]

R0 (2.1.3)

2.2 Observations of Gas Dynamics

◆Peterson et al. 1978, ApJ,219,31

NGC 5383 (SBb)

Observations:

long-slit emission line spectroscopy at various positions (Hα, [NII], [SII])

Stellar absorption line spectroscopy along the bar (Ca II, H,K)

Results:

Emission line velocity field is complex, and not described by pure rotation.

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1)warped disk model fits observation (warp presumably caused by a companion

UGC 8877)

2)planar model with noncircular velocity also fits observation.

◆ Peterson & Huntley (1980,ApJ,242,913)

NGC 1300 (prototypical barred galaxy, SBb)

Observations:

long-slit emission line spectroscopy at various positions (Hα, [NII], [SII])

Stellar absorption line spectroscopy along the bar (Ca II, H,K)

Limitation: Emission regions are restricted to the nuclear region and spiral arms (No

emission in bar region)

Emission line spectra Gas velocity field drawn by eye (Fig.5)

19

- Stellar rotation curve along the bar = steep rise to 1/6 of bar radius (1.9Kpc), after

which rotation velocity is constant.

- Gas rotation curve along the bar

Inner part = steeper than the stellar one (due to lack of random motions

existing in stellar motions)

Outer part = lower than the stellar one (evidence for non-circular motion)

Comparison with models:

Model = Huntley (1980) gas dynamical simulation in the potential of the stellar

N-body model by Miller & Smith (1979)

Fig.5

20

Fig.6

Spiral arm regions: Model agrees with observations

Nuclear region: Model has less steep velocity gradient

Model was improved (‘augmented model’ by adding ‘bulge’ with mass = 5% of the

disk, radius = 1.5Kpc)

nuclear velocity field is better reproduced (Fig.6, Fig.8), because of

appearance of ILRs and resulting change of gas orbits

Offset dust lanes are better reproduced.

21

◆ Sancisi, Allen & Sullivan (1979,AA,78,217)

HI 21cm observation of NGC 5383

Resolution 25”× 37”(and low S/N make the velocity field difficult to determine)

Results:

- HI poor in the bar region.

- Velocity field: outer part = differential rotation

inner part = noncircular motion present (iso-velocity contours

tend to align with bar)

Conclusions:

- HI data are consistent with Peterson et al (1978) optical data.

- Elliptical streaming lines (i.e., noncircular motions) in the bar region and

Differential pure rotation in outer region established.

- Kinematical disturbance due to the companion galaxy is unlikely.

◆ Blackman & Pence (1982, MN, 198, 517)

Motivation: NGC 5383 (Peterson et al. 1978, ApJ,219,31) may be distorted by a

companion.

Emission line (Hα) spectroscopy of isolated barred galaxies: NGC 2525 (SBc) &

NGC 7741 (SBcd)

Accuracy ～15km/s

Model prediction : gas moves on elongated orbits aligned with or at most 45 deg

inclined to the bar v// < v⊥

Velocities along the slit placed on the bar (v//) were found to coincide with velocities

along the slit perpendicular to the bar(v⊥) (for both NGC 2525 and NGC 7741)

circular motion without any deviation

◆ Blackman (1981,MN,195,451)

Long-slit spectroscopy (Hα, NII) of

- NGC 613(SBbc): v// and v⊥ profiles are coincident no non-circular motion.

- NGC 1097 (SBb): spectra are confined to nuclear regions no reliable discussion

on velocity field.

- NGC 1365 (SBb): spectra confined to nuclear region and outer spiral arms (no

spectra for the bar region) no reliable detection of non circular

22

motions, but it may be required to get a reasonable total mass of

this galaxy. (reasonable = consistent with typical M/L)

- NGC 1313 (SBd):pure circular motion cannot explain observations for plausible

inclination and line-of-nodes for this galaxy this galaxy may be

tidally disturbed.

HI 21cm line observations will provide a better picture of velocity field in these

galaxies in future.

2.3 Theoretical Treatments of Gas Dynamics

Modeling of interstellar gas

1) continuous fluid (Huntley et al, 1978,ApJ,221,521;1980,ApJ,238,524)

option: isothermal / radiative cooling / heating due to SN

2) ensemble of clouds dissipating energy by inelastic collisions (Combes & Gerin

1985,AA,150,327)

option: heating due to SN

Theoretical interests:

- gravitational torque & angular momentum exchange

- formation of shock (dust lane)

- gas inflow to the center (fueling activity)

- effect of resonances (ILR, CR, OLR, higher resonances)

◆ Sorensen, Matsuda, Fujimoto(1976,APSS,43,491)

Isothermal fluid in a given bar potential ‘dark lane = shock’

23

◆ Schwarz, M.P. (1981,ApJ,247,77)

Gas dynamical simulation in a given gravitational field

Interstellar gas modeled by inelastically colliding particles (‘sticky particle method’)

(to see difference from stellar response)

Potential: axisymmetric part + bar potential [A(r)cos(2θ)]

Ωb chosen so that there is no ILR

Results:

24

1) collisionless case (stellar response)

Initial spiral arms quickly disappear symmetric distribution (Fig.3)

2) collisional case (gas response) (Fig.4)

- Spiral arms (extending from CR to OLR) last longer than in the collisionless case

- Gas between CR and OLR moves to near OLR ring forms near OLR

25

Why spiral arms appear in gas?

▪ Gas tries to follow periodic orbits

▪ But there are two periodic orbit families near a resonance, which are

elongated perpendicularly and therefore crossing.

▪ Gas orbits cannot cross (difference from stellar orbits)

▪ Gas orbits change their orientation continuously, leading to spiral shape

This spiral configuration allows the bar to exert a torque on the gas and change its

angular momentum

[Compare angular momentum changes (Fig.8 , Fig.9)]

Two types of outer rings: (depending on initial gas distribution)

- parallel to the bar uniform gas distribution extending well beyond OLR

- perpendicular to the bar more concentrated distribution

(Most observed outer rings are perpendicular to the bar, e.g., Kormendy,

1979,ApJ,227,714)

◆Schwarz (1984, MN, 209, 93)

Effect of bar strength and pattern speed

26

Gas particles experiencing energy dissipation (inelastic collisions)

ほぼ定常状態に落ち着いたところで粒子分布を比較した。

As bar becomes stronger,

- arm-interarm density contrast and pitch angle of spiral arms increase.

- bar の両側の空白域が広がる。

As the pattern speed decreases

Spiral arm ring at CR (4/1 resonance)(<->inner ring?) ring at ILR (<->

nuclear ring?)

◆ Sander & Tubbs (1980, ApJ, 235,803)

Gas dynamical simulation in a given gravitational potentail

Motivation: understanding observed kinematics of NGC 1300

Models: three components

1) central disk ( ⇔ disk): Kuz’min-Toomre disk (mass Md, length scale rd,

maximum rotation velocity Vmax)

2) triaxial homogeneous ellipsoid ( ⇔ bar): (x/y/z semiaxes = a/b/c, mass Mb)

3) extended disk ( ⇔ halo): Kuz’min-Toomre disk (mass Me =3.17 Vmax 2a/G,

length scale re=4a) (this choice was made to get a flat rotation for a<r<4a)

Independent parameters: Mb /Md, b/a, c/a, rd /a, rc /a

[rc: corotation radius i.e. Ωb=Ω(rc)]

Simulations in five-parameter space

Standard model : Mb /Md=0.53, b/a=1/4, c/a=1/4, rd /a=0.3, rc /a=1.1

(Hereafter b=c, because z-scale height does not affect the result significantly)

Compare models with observation

Keys of observed gas morphology (NGC 1300)

1) offset linear dust lanes on leading edges of the bar extending the whole bar length

2) spiral arms originating perpendicularly from the bar ends

3) bright large HII regions near the bar ends

Keys of observed gas kinematics (NGC 5383)

1)circular motion with constant velocity beyond the bar

2)iso-velocity contours skewed parallel to the bar in within bar radius

27

1. Comparison of morphology (Fig.3.4.5.6)

1) Mb /Md sequence

As Mb /Md increases: open spiral arms gas bar with offset lanes too small

offset

⇒ 0.4<Mb /Md<1.0

28

2) b/a sequence

As b/a decreases: open spiral arms gas bar with offset lanes too small offset

⇒ 1/5 < b/a < 1/3

29

3) rd /a sequence

For large rd /a, offset dust lanes become less conspicuous

⇒ rd /a < 0.5

4) rc /a sequence

Small rc /a curved dust lanes, large rc /a entire gas response rotated with

respect to the bar

⇒ 1.0 < rc /a < 1.5

Standard model satisfies all the three morphological requirement.

30

2. Comparison of kinematics

Standard model velocity field ⇒ elongated streaming in the bar region

Best fit to the observation given by the standard model in which rc /a was modified to

1.2 ⇒ skewing of velocity contours successfully produced.

31

◆ Athanassoula (1992,MN,259,345)

Dust lane morphology

Hydrodynamical simulation for isothermal gas

- Depletion of gas by star formation

- Supply of gas by infall

Potential: bulge + disk + bar

Parameters:

bar mass

bar axial ratio

bar pattern speed

bar central concentration

Results:

1) offset dust lane requires existence of x2 orbit family

shape of dust lane gradual shift of orientation of flow lines from x1 to x2 orbits

2) offset shock of observed shape constraints on model parameters

- pattern speed: rL=(1.2±0.2)a (a=bar major axis, rL =Lagrangian radius)

smaller rL (larger Ωb) centered shock, larger rL ‘convex’ shock

- central concentration: too low centered shock, too high ‘convex’ shock

- large axial ratio (b/a) or low bar mass curved shock (NGC 1433 type), small

axial ratio straight shock (NGC 1300 type)

32

Rings

◆ Athanassoula et al. (1982,AA,107,101)

Ring sizes measured by de Vaucouleurs & Buta (1980, AJ, 85, 637)

Outer-to-inner ring ratio

33

Assume 0.7<δ<1.0 (typical for Sa and Sb analysed in this paper)

34

strongly barred galaxies : outer ring = OLR, inner ring = CR or UHR

consistent with theoretical results (Schwarz, 1981, ApJ, 247,77)

- bar just extend to CR

- inner rings form just inside CR, and outer rings just outside OLR

◆ Byrd et al (1994, AJ, 108, 476)

Gas dynamical simulations in a given gravitational potential

Gas initially distributed to around OLR

Pattern speed (Ωb) varied

- fast no UHR , no ILR

- medium UHR, no ILR

- slow UHR, ILR

1)Two types of outer rings

R1 ring form quickly after that R2 ring appears (for all Ωb)

Different from Schwarz’s results

Reasons : More particles were used

Different treatment of energy dissipation

Longer evolution was traced

Obs. IC 1438 : two outer rings

R1 is prominent in I band, whereas R2 in B band!

2) as Ωb decreases

R2 becomes relatively less prominent

Inner rings (UHR), offset dust lanes, Nuclear rings appear (ILR)

nuclear rings should accompany R1 more often than R2

Buta & Crocker (1991, AJ, 102, 1715)

11 R1 galaxies 9 show nuclear star formation and offset bar dust lane

11 R2 galaxies 3 show nuclear star formation or offset bar dust lane

35

36

2.4 Star Formation and Activity

◆Hawarden et al. (1986 MN, 221, 41p)

Sample: all RSA galaxies

with S0/a-Scd type designation in RC2

with detection in four bands (12μm, 25μm, 60μm, 100μm) in IRAS

(Seyfert1, Seyfert2, LINERS excluded)

186 galaxies

1) Barred galaxies have excess of F25 relative to F12 and F100

starbursts in barred galaxies

Check

Model SA galaxies + IRAS observed fluxes of Galactic HII regions

agree with SB galaxy FIR colors

2) Starbursts are concentrated in nuclei, because

- Disks of SA and SB are similar

- unresolved HI sources (21cm continuum) are observed exclusively in barred

galaxies (Hummel, 1981, AA, 93, 93)

◆ Aguerri (1999,AA,351,43)

sample: 29 Sb-Sd galaxies (4 Sb + 25 later types)

= Martin (1995) sample + Sb-Sd galaxies from RC3 – galaxies with companions

[Companion = a galaxy within projected distance of 500 kpc and systemic velocity

difference of 500 km/s]

37

No AGN

Bar parameters:

- Projected ellipticity (10(1-b/a)) ellipse fit to V band NED images

- relative bar length (Lb/D25)

Star formation activity = IRAS fluxes I25/I100

Results:

- ellipticity correlates with I25/I100

- relative length affects little

38

Spatial distribution of FIR emissions

- IRAS have insufficient resolution to locate star forming regions

- Devereux (1987, ApJ, 323, 91) see no strong concentration of FIR emission for late

type barred galaxies (Sbc-)

◆Devereux (1987, ApJ, 323, 91)

Spatial distribution of 10μm luminosity

Ground-based observation (IRTF 3m telescope) + IRAS

Sample:

- 133 galaxies taken from Nearby Galaxies Catalog (Tully 1987)

(Vhel < 3000 km/s for this catalogue)

- inclusion in IRAS catalogue

- RC2 morphological and bar classification

- No interacting galaxies

- L60μm > 2.2☓109 L◉ (for completeness) LFIR(40-120) > 2.9☓109 L◉

Divided into barred (SAB,SB) and unbarred (SA) galaxies

into early (-Sb) and late (Sbc-) types

Central (typically < 500 pc) 10 micron luminosity by 3m NASA IRTF

Luminosity:

39

Early types : barred galaxies have larger L10μm than unbarred ones.

Late types : no difference

Compactness of emission:

(= Ground-based small-beam 10μm flux/ IRAS larger-beam 12μm flux)

early types: more compact in barred than in unbarred galaxies.

late types : no difference

40

Infrared colors (IRAS S25/S12):

early types: barred galaxies have larger S25/S12 than unbarred ones

( S25/S12 correlates with compactness)

late types : no difference

Source of emission: Seyfert activity and/or star formation (cannot be segregated

because Seyfert 1, Seyfert 2, and HII overlap in α(100,60) vs α (60,25) diagram)

◆ Simkin,Su,Schwarz (1980,ApJ,237,404)

Seyfert activity in barred galaxies

All spiral and lenticular galaxies from RC2 with Vhel<5000km/s and morphological

classifination

1) Seyfert slightly prefer B and AB

2) Seyfert prefer (rs) and (r)

3) Seyfert much prefer (R) and (R’)

Schwarz’s simulation

Bar inner (r) and outer (R) rings

Bar gas infall to the center

41

Seyfert without bars may be triggered by tidal interactions

◆Hunt & Malkan (1999,ApJ,516,660)

Extended 12 micron Galaxy Sample (E12GS, Rush et al. )

891 galaxies (mostly disk galaxies)

Selection effect? (because 12 micron selection may favor star formation activity)

Yes, but not so strong as to affect conclusions.

Activity class, morphological types, bar/ring classes, major and minor diameters,

from NED (NED Morphology is largely from RC3)

Morphology

Seyfert 1: median =Sa, Seyfert2: 2, LINER: 3.5, HII:3, normal: 4

Normal galaxies in E12GS have similar axial ratios, morphological types, bar and

ring fractions to other n ormal spirals.

42

- HII/starburst have higher fractions of bars (SAB+SB:82-85%)and peculiar

morphplogy

- Seyfert/LINERs have the same bar fraction(61-68%) as normal galaxies(68-69%),

but

higher incidence of rings (Seyfert: outer ring 40% opposed to 10% in normal 12

micron galaxies, LINER: inner ring 57% vs 40%)

Morphological effects? (because rings and Seyferts are both more frequent in

early type galaxies)

Consider only T<=2

Outer ring: normal=24%, Seyfert1=60%, Seyfert2=50%

Inner ring: normal=43%

( evolution scenario: bar formation gas inflow nuclear starbursts

LINER/Seyfert)

Bar fraction and morphological type (Fig.3)

- normal galaxies: bar fraction is constant except very late types (T>6),

which show high bar fractions (86%)

- HII and Seyfert 2: bar fraction is constant

- Seyfert1- bar fraction has a peak (90%) at T=3

43

◆ Chapelon et al. (1999,AA,345,81)

Two sample of barred galaxies , R band photometry

1) barred Markarian galaxies with IRAS detection

2) barred Frei et al. (1996) galaxies

44

1)+2) are classified into active (log(S25/S100)>-1.2) and normal galaxies

(most of Markarian and some Frei galaxies have also designation as starburst or

Seyfert)

Bar measurement:

- Bar length a (determined by eye from bar major axis profile)

- Bar width b (at a/2): distance from bar major axis to the same isophotal level as the

bar end (to avoid influence of bulge)

Galaxy diameter Dc from LEDA

Early type bars are long and strong regardless of active/normal

Late-type bars in active galaxies are longer and stronger than those in normal

galaxies

45

46

Central Oxygen abundance

Longer bars smaller O/H

(Probably due to dilution by bar)

◆ Ho,Filippenko,Sargent (1997,ApJ,487,591)

Sample: 319 spiral galaxies with

T=0-9 (S0/a-Sm), BT <12.5 mag, δ>0°

Bar morphology : SA,SAB,SB from RC3

Observation: spectroscopy of nuclear region

Moderate-resolution (2.5-4Å) long-slit spectra

Aperture 2”☓4” (typically 180pc ☓ 360pc)

(so may miss starburst nuclear rings typically with several 100 pc size)

47

Ho et al. 1997,ApJS,112,315

- Sample classified into HII nuclei & AGNs based on line strength ratios

(in similar manner to Veilleux & Osterbrock,1987,ApJS,63,295)

- Activity strength : luminosity L(Hα), equivalent width EW(Hα)

Results:

1) Barred and unbarred galaxies have similar luminosities in each Hubble type.

2) star formation activity in barred galaxies stronger than unbarred galaxies

only for late-types (Sc-Sm). (seems to contradict Devereux 1987, but is not

discussed)

3) AGN activity similar in barred and unbarred galaxies both for early (S0/a-Sbc)

and late (Sc-Sm) types.

Implication: Bar does not affect AGN activity. AGN are fueled by local processes

like tidal disruption of star by BH or stellar mass loss

◆ Laurikainen,Salo,Buta (2004,ApJ,607,103)

Sample: 149 OSUBGS + 22 2MASS spirals

- Inclination < 60°

- BT<12.0

- RC3 type 0<T<9 (early T=0-3, late T=4-9)

- -80° < δ < +50°

Classification into active and nonactive subsamples based on NED (which mostly

rely on emission line ratios: Veilleux & Osterbrock 1987, ApJS,63,295)

Hereafter AGN = Seyfert + LINERS

Bar fraction by

1) RC3 classification

AGN have similar bar fraction ( SB+SAB ) to nonactive galaxies

HII/starburst have marginally larger bar fraction than nonactive galaxies

2) EFP02 B-band classification

Same as 1)

3) EFP02 H-band classification

48

Same as 1) but

SB fraction is larger (67-72%) in Seyfert,LINER,HII than in non-active(58).

4) Fourier method for H-band images (m=2,4 components with phases nearly

constant)

SB fraction is larger (69-72%) in Seyfert,LINER,HII than in non-active(55).

bar fraction depends on the method of identifying a bar.

Fourier method picks up relatively strong bars (like SB).

Past near-IR studies

- KSP00,LSKP02: Bar fraction in Seyferts is higher than in non-active.

- MR97: Bar fraction in Seyfert similar to that in non-active. (reason: visual

identification of bars lead to inclusion of SAB into bar fraction. SAB fraction

in Seyfert is smaller than in non-active according to present work, which

explains discrepancy)

Bar strength statistics (Fig.8)

49

- early-type bars are longer, more massive (i.e., larger A2), and have weaker

strength (i.e., smaller Qg) than late-type bars.

- Qg increases as A2, but correlation is shallower for early-type bars.

- Bars in Seyfert and LINER have weaker strength (Qg) than bars in HII or

non-active galaxies (Seyfert and LINER preferentially occus in early-type

galaxies, whereas HII galaxies are generally late-types)

- Bulges dilute Qg (Fig.11) but do not affect length (Fig.12) and mass (Fig.13) of bars

much.

- Some late-type bars exist with large A2, large Qg, and small rQg/Rbar.

These bars are generally non-active. (Fig.16)

50

51

2.5 Chemical Compositions (Radial Mixing of Disk Matter)

Abundance gradient (Metallicity generally decreases outward in unbarred galaxies)

◆ Vila-Costas & Edmunds (1992, MN, 259, 121)

30 galaxies with published HII region emission line strength

(O/H) was calculated

Morphological types (Hubble types and bar types) taken from RC2

Results:

- barred galaxies have smaller gradient than unbarred galaxies

- unbarred galaxies: later types have steeper gradient than early types in [dex/kpc]

but difference vanishes if normalized by R25

52

◆ Martin & Roy (1994, ApJ, 424, 599)

Spectroscopy of HII regions in 3 galaxies to get their metallicity

(other measured galaxies from the literature also included in the analysis)

More quantitative evaluation of bar strength

Visual measurement (on Sandage-Bedke Atlas) of

Bar semi-major axis a and bar ellipticity EB≡10(1-b/a)

(both are inclination corrected)

53

Gradient becomes flatter as bar length increases

54

Gradient becomes flatter as bar ellipticity increases (stronger than bar length

dependence)

dilution by bar-induced gas inflow

(but star formation should be maintained at low level)

Stellar population gradient

◆ Gadotti & Dos Anjos (2001, AJ, 122, 1298)

- UBV color profiles of 257 Sbc barred (SB,SAB) and unbarred (SA) galaxies

from aperture photometry in published data (Longo & de Vaucouleurs, 1983, 1985,

Univ. Texas Monogr. Astron. No.3, No.3A)

- Bar morphology from RC3

U-B, B-V color gradient: (no external or internal correction)

total and bulge colors:

1) color within the smallest aperture = bulge color

color within R25 aperture = total color

2) bulge color

(color within 1/5 effective radius of the galaxy)

total color

(color within 2 effective radius)

(G = color gradient)

= color index at B-band effective radius given by RC3 - Galactic reddening correction

with E(B-V) given by Schlegel et al. (1998, ApJ, 500, 525)

- internal extinction

I band (Giovanelli et al. 1994, AJ, 107, 2036)

where a and b are galaxy major and minor axes (log(a/b) given by R25 in RC3)

AU,AB,AV = (3.81,3.17,2.38)☓AI

(Elmegreen 1998, in ‘Galaxies and Galactic Structure’ ed. Englewood, Cliffs)

55

These values were checked by independent CCD observation of 14 galaxies

barred galaxy G(U-B) (both for face-on and edge-on) are smaller and wider

AGN fraction (Veron-Cetty & Veron 1998, ‘Quasars and Active galactic Nuclei’)

8% for negative gradient (G<-0.1)

36% for positive gradient (G>0.1)

(both for U-B and B-V)

Colors reflect both age and metallicity

No correlation with metallicity gradient Fig.7

(Martin 1995, AJ, 109, 2428; Zaritsky et al., 1994, ApJ, 420, 87)

56

colors reflect ages (effects of dust also possible)

One interpretation

1) Galaxy forms through monolithic scenario (lower-left of Fig.7)

2) Bar forms ( lower right)

(because abundance gradient becomes shallower, but color gradient hardly changes,

because timescale for gas inflow is shorter than the time required for star formation

in the center)

3) Star formation starts in the center ( upper right)

4) Bar destruction by accumulated material

Gas inflow stops ( upper left)

5) Star formation stops ( lower left)

6) 2)

Color gradients have no correlation with bar parameters (by Martin 1995)(Fig.8)

Bulge colors

total color is the same for all gradient classes

bulge is bluer as G increases

57

58

Bulge and total colors are correlated in both negative and positive gradient cases

But, bulge colors are systematically bluer for positive case

59

§3 Dynamics of Bars

Numerical simulations have extensively been used to clarify bar dynamics.

3.1 Bar Instability

◆ Ostriker & Peebles (1973, ApJ, 186, 467)

'Rotating massive disks are generally unstable and produce bars spontaneously'

Ostriker-Peeble criterion : Trot/|W| > 0.14 unstable

where Trot = kinetic energy, W = potential energy

How to suppress instability

1)Increase random motion (and reduce rotation) in disk so that Trot ↘

2)Increase halo mass so that $W ↗

◆ Hohl (1976,AJ,81,30)

Stabilizing effect of halos

Disk: (Q=1)

Halo: rigid sphere of uniform density

60

Conclusions:

61

1)point-mass like halo needs 60% of total mass to suppress bar instability.

2)more extended halo is more effective, requiring 40% of total mass.

◆ Athanassoula & Sellwood (1986, MN,221,213)

Stabilizing effects of random motions as well as massive halos

Models:

Disk : Σ(r)=Mf

2πa2 (

r2

a2 +1)

-3/2 (cutt off at 〜5a)

(M: total mass, f: disk mass fraction, a: disk scale length)

Bulge (rigid): ρ(r)=3M(1-f)

4πb3 (

r2

b2 +1)

-5/2 [M(1-f): bulge mass, b: bulge scale

length = a]

Distribution function (equilibrium solution of collisionless Boltzmann equation)

1) Miyamoto models (1971, PASJ, 23,21)

2) Kalnajs models (1976, ApJ, 205, 751)

Bar was extracted by Fourier analysis for early evolutionary states

Exponential growth rate was determined for linear growth phases

62

growth rate = 0.169q-0.092σu

<v> -0.048

Conclusions: pressure support (stellar random motions) reduces the halo mass

required to inhibit bar instability in real galaxies.

◆ Berman & Mark (1979,AA,77,31)

‘Small but compact’ bulges are sufficient to stabilize disks

(i.e., massive haloes not necessary)

- pure disk simulation (Kuzmin disk with Q=1) strong bar

- inner disk part was replaced by rigid Plummer sphere (i.e. bulge) with mass 0.3 and

scale length 1/ 10 of the disk (i.e., disk mass = 0.7) no bar

3.2 Parameter dependence of bar properties

◆ Sellwood (1981,AA,99,362)

Dependence on shape of rotation curve

Models:

Disk : Σ(r)=Mf

2πa2 (

r2

a2 +1)

-3/2 (cut off at 2a)

(M: total mass, f: disk mass fraction, a: disk scale length)

Bulge (rigid): ρ(r)=3M(1-f)

4πb3 (

r2

b2 +1)

-5/2 (M(1-f): bulge mass, b: bulge scale

length)

[This bulge is highly concentrated to the center, and not intended to represent

massive halo]

f=0.75, Q=1

0.3<b/a<1 ( different rotation curves Fig.2)

63

64

Bar length LB = the radius at which m=2 Fourier component drops sharply and begins

to change phase with radius.

LB is larger for more slowly rising rotation curve

LB growth is larger for initially shorter bar (because more matter is available

outside bar, which absorbs bar angular momentum and helps bar growth)

Gravitational softening stabilizes disk considerably.

Stable model by Berman & Mark (1979,AA,77,31) is affected by too large

gravitational softening.

1) No theoretical interpretation is possible for the correlation between rmax and bar

length

.

2) Observational implications:

Models correspond to early-type galaxies (with 25% mass in bulge)

Obs: Athanassoula & Martinet (1980, AA, 87, L10) bar length and bulge size

Galaxies (earlier than Sbc) from Kormendy (1979,ApJ,227,714)

- Bulge radius measured at a constasnt surface brightness by Kormendy.

- Deprojection of bar length using inclination and line-of-nodes obtained assuming

that inner rings or lenses are flat circles. (outer disk may be warped)

- D0 ≡diameter at 25 mag/arcsec2 in B band

65

Good correlation What determines bar-size?

Lynden-Bell (1979, MN, 187,101), Contopoulos (1980, AA, 81,198)

Bars and Hubble types

◆ Combes & Elmegreen (1993,AA,271,391)

Claims realization of early and late type bars

Disk+bulge numerical simulations

- Stellar disk : Toomre disk (mass Md, scale length ad)

- Gas disk : exponential disk (scale length 8kpc)

(Both disks truncated at Rd)

- Bulge : Plummer sphere (mass Mb, scale length ab)

66

Model parameters

ab ad Mb Md Rd Q

Late-type models

CS1: 3 10 2 23 15 1.5 (small low-mass bulge)

CSE: 30 10 20 20 30 1.5 (massive halo)

PSG1: 3 10 2 23 25 Q(r)(polar grid model)

Early-type models

CS2: 1.5 6 16.67 8.33 15 0.0 (massive bulge and concentrated disk)

CSG2: 1.5 6 16.67 8.33 15 1.5

PSG2: 0.5 6 5 30 25 Q(r)(polar grid model)

Late-type models generally characterized by slowly rising rotation curve (Fig.2),

and early-type models by rapidly rising rotation curve (Fig.7)

67

Fig.9 Bar difference

Early-type: bar length = 6.2 kpc, flat density profile within 3 kpc

Late-type: bar length = 9 kpc, exponential profile

Gas response

[Limitations:

-no halo component was included early-type models have smaller disk mass

68

fraction and more stable (inclusion of halo may invert this situation)

- bar length relative to disk size is not shown to match the observed trend for

different Hubble types

]

Effects of halo concentration

◆ Athanassoula & Misiriotis (2002,MN,330,35)

Numerical simulations intended for comparison with observations

Model parameters have been widely varied

Disk:

Bulge:

Halo:

Disk: Md=1, h=1 (disk cutoff at 7.5), Q=0.9

Halo: Mh=5, rc=10

Bulger: Mb=0.6, a=0.4

(all components were modeled by particles)

Model MH (‘massive halo model’): γ=0.5 (no bulge)

Model MD (‘massive disk model’): γ=5 (no bulge)

Model MDB (‘massive disk with bulge’): MD + bulge

69

MH MDB MD

1) Bar length decreases 2) Bar becomes fatter 3) Edge-on shape: X boxy

Bar shape analysis

70

◆ Athanassoula (2003,MN,341,1179)

Bars in halo/bulge-dominated systems stronger than bars in disk-dominated

systems.

Why?

Isolated disk galaxy evolution

- Inner disk emit angular momentum by resonant stars

- Emitted angular momentum is absorbed by resonant stars in outer disk, halo, and

bulge.

This prediction by linear theory (Lynden-Bell & Kalnajs, 1972, MN, 157,1) is

confirmed by numerical simulations for non-linear cases.

Fig.1 : disk+halo model

(here, resonant stars are found by calculating Ω and κ by spectral analysis,

so strictly speaking, existence of resonant orbits does not necessarily mean the

existence of resonance itself)

- Colder and massive components are more effective in emitting and absorbing

angular momentum

- As angular momentum is lost, bar becomes longer, thinner and pattern

speed decreases.

71

bar becomes stronger (longer and thinner) and slows down more quickly,

as halo and/or bulge mass increases

§4 Origins (Formation) of Bars

4.1 Bar instability

4.2 Tidal Triggering

◆ Noguchi (1987, MN, 228, 635; 1988, A&A, 203, 259)

Close Encounter simulations for disk+halo galaxy models

'Even stable galactic disks make bars under the influence of tidal

forces from another galaxy'

◆ Byrd & Valtonen (1990, ApJ, 350, 89)

Bar formation by galaxy cluster tidal field ( S0 and AGN in galaxy cluster)

4.3 Bar incidence in various environments

◆van den Bergh (2002, AJ, 124, 782)}

Sample: Northern 930 Shapley-Ames galaxies divided into

(1) field, (2) group, or (3) cluster environments.

based mainly on inspection of Palomar Sky Survey prints.

Barred or non-barred classified by two competent morphologists, using blue images.

Results on bar fraction:

- field : 25 ± 3 %

- group : 19 ± 4 %

- cluster : 28 ± 3 %

Caution : Morphology-Density Relation (Dressler 1980, ApJ, 236, 351)

Not affected by different morphological mix in different environments.

For Sc and SBc,

- field : 17 ± 3 %

- group : 12 ± 5 %

72

- cluster : 25 ± 5 %

Bar frequency not dependent on environments

Bar formation determined by intrinsic properties of parent galaxy.

◆ Thompson (1981, ApJ, 244, L43)

Sample: Coma Cluster galaxies with diameter > 16”

1) Bars occur twice as often in Core (r<28') as in Annulus (mean r=50')

or Outer Area (mean r=98')

2) No difference in luminosity distribution between bars and nonbars.

◆ Elmegreen, Elmegreen & Bellin (EEB, 1990,ApJ, 364, 415)

Sample

1) Binary sample :

- Turner binary(1976, ApJ, 208, 20)(87 galaxies) : selected by angular separation

- Peterson binary(1979, ApJS, 40, 527)(227 galaxies) : selected by angular

separation and magnitude difference

2) Group sample :

- Geller & Huchra group (1983, ApJS, 52,61)(460 galaxies) : selected by velocity

difference and projected separation (using CfA Redshift Survey)

D12 = 2 sin (Θ/2) V/H0 < DL, where V = (v1 + v2)/2

V12 = |v1 - v2| < VL

- Turner & Gott group (1976, ApJS, 32, 409)(221 galaxies): procedure complicated

but based on position alone.

3) Field sample : Turner & Gott (1976, ApJS, 32,409)(119 galaxies)

4) All spirals : RC2

Morphology : RC2 and UGC

Results:

1) Higher bar fraction in binary sample only for early morphological type (Fig.1)

2) Smaller galaxies in binary tend to be barred.

3) Excess of early-type galaxies in binary systems. (Fig.2)

73

74

Scenario:

Interactions turn perturbed galaxies into barred-and-earlier-type (Table 4)

◆Giuricin et al. (1993, ApJ, 407 22)}

improvement of EEB's analysis (introduce objective environmental parameters)

Sample: Nearby Galaxies Catalogue (Tully 1988)

= Shapley-Ames Catalogue (magnitude-limited, Sandage & Tammann 1981)

+ all-sky HI survey (diameter-limited, Fisher & Tully 1981, ApJS, 47,139 ;

Reif et al. 1982, A&AS, 50, 451)

2367 galaxies (Table 2)

Morphology : RC3 morphology

Local Galaxy Density Parameters

Distances :

- non-cluster galaxies = radial velocity

- cluster galaxies = mean velocity of the cluster

75

1) ρσ

ρi,σ = C exp[ -ri2/2(F1/3σ)2 ] (C = 1/(2π)3/2^3 and F is incompleteness)

ρσ = ∑iρi,σ (∑ is taken over galaxies with MB ≤ -16)

2) CR : number of galaxies with MB ≤ -16 and distance less than R, divided by

4πR3/3

3) distances d1 (d2,d3,...)$ of the first (second, third,...) nearest galaxy

Results:

1) Early types (Sa-Sab) : bar fraction larger in denser environments (in terms of ρ

0.25, C0.5, and d1) (Fig.5, Fig.9)

2) Late types (Sb-Sm) : bar fraction not dependent on environments (Fig.6, 7, 8)

3) Result 1) is due to less luminous (MB > -20) early type galaxies (Fig.11)

4) For 1Mpc< scale, no dependence is observed for any morphological types

Fig.5

Fig.6

76

Fig.7

Fig.8

Fig.9

77

Fig.11

Interpretation:

These results agree with interaction scenario, because

1) Less massive galaxies tend to have more massive companion.

2) Less massive galaxies tend to have more gently rising rotation curve.

And these two characteristics are favorable to tidally-triggered bar formation

(Noguchi, 1987, MN, 228, 635).

§5 Evolution of Bars

5.1 bending boxy/peanuts bulges

Predicted by numerical simulatins

◆ Combes & Sanders (1981, AA, 96, 164)

垂直方向の resonance (特に Inner Lindblad Resonance) によって、 粒子が垂直方向の

速度成分を増加させるため, バーは box/peanut shape に。

Supporting observations

◆ Lütticke et al. (A&AS, 145, 405 ,2000)

Statistics of box- and peanut-shaped bulges

Previous studies: incomplete (or inhomogeneous) samples

>1000 edge-on galaxies from RC3

- D25>2’, -3.5 < T < 9.5

- Nearly edge-on galaxies (logR25>0.3 for T≤-0.5, logR25>0.35 for others)

(limitation by diameter is better than by magnitude, because RC3 claims

completeness for D25>1’, also magnitude limit will bias for early-type galaxies)

78

Inspection of Digitized Sky Survey images (B,V,R)

Classification into box/peanut or elliptical bulges

45% of all bulges are box/peanut-shaped (>40% from S0 to Sd)

box/peanut-shaped bulges (so numerous）are edge-on bar

79

◆ Lütticke et al. (A&A, 362, 435 , 2000)

JHK (K’) observation of 60 edge-on galaxies

bar/bulge length ratio ↗

as elliptical (4) box-shaped peanut(1) (Fig.4)

N-body simulations (i.e, difference in viewing angle)

(inner region = bulge + thin bar + b/p structure)

Another signature of bars in edge-on galaxies

◆Athanassoula & Bureau (1999, ApJ, 522, 699)

Isothermal gas

Potential：Athanassoula (1992,MN,259,328;MN,259,345)

80

Characteristics of PV (position-velocity) diagram

1) Model with ILR

- Steep feature nuclear spiral

Peak velocity is maximum when ψ=90°(bar seen side-on), because gas

nearly follows x2 orbits

- Less steep feature circular rotation of gas outside bar

Feature not dependent on ψ

- Bar region (e.g., offset shock and spiral arms just outside bar) do not

contribute to PV diagram because of small associated mass

2) Model without ILR (i.e., without x2 orbits)

- Steep feature is lacking (absence of x2 orbits leads to no nuclear spirals)

81

Observed bar signatures

- Gap between steep and less steep features ( paucity of gas in bar region)

- Viewing angle of bar (max velocity of nuclear component / velocity in the outer

component)

[In case of no ILR very difficult]

◆ Bureau & Freeman (AJ, 118, 126, 1999)

17 boxy/peanut bulges

Hα long slit spectroscopy (along the major axis) to investigate gas kinematics

Results:

14 out of 17 B/P galaxies have a bar

None of spheroidal bulges is associated with a bar

82

IC 4937 : peanut ψ=90°, large nuclear/outer velocity ratio

NGC 1886 : boxy ψ=0° , small velocity ratio

5.2 Dissolution of bars by growth of central mass

(注意： bending instability と区別せよ！)

◆Hasan & Norman (1990, ApJ, 361,69)

2D orbit surface of section

Results:

fraction of phase space occupied by regular x-1 orbits decreases as the central

core mass increases.

Physical insight:

epicyclic theory x-1 orbit exist only between outer ILR and corotation.

As the central mass increases, ILR appears and moves outward finally to the bar

end (=CR), so that the region where x1 family exists shrinks.

◆Hasan & Norman (1993, ApJ, 409,91)

orbital study in a given 3D potential

characteristic diagram and surface of section

Results:

from 2D orbit study: as the central core mass increases, radial ILR appears

x1 orbits become unstable (stochastic) bar dissolution

(具体的なメカニズムは言及せず。ILR の出現と instability を関連させているだけ)

from 3D orbit study: radial ILR is close to vertical ILR help heating of disk

stars into a bulge.

83

◆Norman, Sellwood, Hasan (1996,ApJ,462,114)

銀河の総質量の 5% の central mass によって短時間(1 bar rotation) に bar が壊れる。

N-body simulations

Mass ratio: Disk 75%, bulge+core(rigid components) 25%

After bar has fully formed and settled into boxy shape due to bending instability,

radius of core decreases gradually (over about 4 bar rotation periods) with mass

fixed

bar vanish suddenly (Fig.2)

new axisymmetric ‘bulge’ is not boxy but somewhat peaky (Fig.8)

Reason: (revealed by ‘Surface of section’)

- Boxy/peanut bars are supported by 2:2:1 orbit family, which is analog of x1 family

in 3 dimensions (these bars are essentially the same as 2D bars)

- As the core shrinks, bar-supporting stellar orbits (x1 orbits) become stochastic

(resonance との関係は言及なし)

Fig.2

84

Surface of Section:

Core mass = 0%

Core mass = 3%

85

Comment on other ‘explanation’

‘ Orbit scattering by the central core’ (Norman, May, van Albada,

1985,ApJ,296,20)

This explanation applies only to slowly rotating case, in which ‘box’ orbits

are predominant. Box orbits pass near the center.

But in rapidly rotating case, loop orbits (like x1 orbits) are dominant.

Loop orbits avoid the center.

Supporting observation?

◆ Carollo et al. (2001, ApJ, 546, 216)

HST V,H,J observation of R1/4 and exponential bulges

結果： late-type spiral に見つかった全ての Exp bulges は central nuclei という

compact な component を持つ。luminosity から mass を推定してみると,これ

らの nuclei は 'massive enough to dissolve progenitor bars'である。 また、

nuclei の color からそれらは母体の Exp bulge と似た stellar population を

持つと推測される。

5.3 Nested bars or 'Bars-within-bars'

86

◆ Shlosman, Frank, & Begelman (1989, Nature, 338, 45 )

'Bars-within-bars' scenario for AGN fueling

large-scale bar gas inflow central massive gas disk central (secondary)

bar and so on..... (= bar instability cascades to successively smaller scales)

◆ Kormendy (1993,IAUS,153,209)

'Kinematics of extragalactic bulges: evidence that some bulges are really disks'

- many bulges of barred galaxies well above 'the oblate line' in

V/σ-ε diagram. (Fig.3)

- barred galaxy bulges tend to be located below Faber-Jackson relation. (Fig.6)

disk-like or triaxial bulges

◆ Elmegreen et al.(1996, AJ, 111,1880)

Near-Infrared Observations of Isophotal Twists in Barred Spirals

1) Sample 1: JHK photometry of 12 barred galaxies (also B,I for 9 galaxies)

ellipse fit

twist ≡ position angle change of >10° from ‘inner region’ to bar end

(Bar end is determined by image and contour map)

2 types of twists

continuous change of PA = triaxial bulge

discontinuous jump between two values = bars-within-bars

2) Sample 2: NIR samples from literature

3) Sample 3: B photograph of barred (SB) galaxies in Sandage & Bedke Atlas

eye inspection

Results (以下では nested bars と triaxial bulge は区別せず)

- Twists are seen only in early-type(-Sbc) spirals

- Twists are seen in some of flat bars, but not in exponential bars

Twist is related to ILR, where stellar orbits change from x2 to x1.

(consistent with other resonance indications: nuclear rings supposed to be

related to ILR are found in SBbc and earlier but not in later-types)

- Flat bars have ellipticity increasing with radius, but exponential bars

have a constant ellipticity

87

88

◆ Friedli & Martinet (1993、AA, 277, 27)

Double-bar numerical experiments

Some models include rigid massive halos

No star formation included

Model(I): small unstable stellar disk + large unstable stellar disk

(expectation: small bar appears after that (or simultaneously) large bar appears.

the small disk creates ILR for the primary bar)

only small bar forms (large bar never develops)

because

small bar large spiral arms large disk heats up no large scale bar instability

Model(II): Model(I)+large gas disk

large and small bars form simultaneously in 1Gyr (10 bar

rotations)

double-barred state lasts for a few bar rotation

small bar dissolves (due to gas accretion to the center) but large bar remains

Model(III): similar to Model(II) but with different parameters

large stellar bar forms (in 1 bar rotation)

small stellar bar forms (after a few bar rotation)

double-bar state lasts for a few bar rotation

both bars weaken because of gas accumulation

1) two bars rotate with different pattern speeds in Models (II) and (III).

2) double-barred state is transient.

3) dissipative component and moderate ILR are essential in forming double bar

systems.

89

90

◆Wozniak et al (1995,AAS,111,115)

BVRI photometry of (not necessarily barred) 36 galaxies (=candidates for having

misaligned secondary bar or triaxial bulge) strongly biased sample

Analysis = ellipse fitting

Define three types of structures based on radial behavior of e & PA (in projected

image)

1) Bar: emin↗ emax↘ emin, PA=const

2) Bar-within-bar : emin↗ esmax↘ emin, PA=const (secondary bar), emin ↗ ep

max↘

emin, PA=const (primary bar)

3) Barred plus twisted isophotes : emin↗ es↘ e’, PA changes (twisted structure), e’↗

emax↘ emin, PA=const (bar)

Bar length (lp, ls) = distance (semi-major axis) from center to emin

(emin length > visual estimate > emax length)

Bar luminosity (Lp, Ls) = luminosity inside isophote of semi-major axis (lp,ls)

Ratios: β ≡lp/ls, γ ≡ Lp/Ls

Uncertainty arises from

- High inclination of the galaxy

- Pixel size

- Seeing

- Dust

Results:

B+B 3.7<β<18.0 2.0<γ<7.5

B+B+B, B+T+B 4.8<β13<13.6 2.3<γ13<7.7 (1.8<β12<3.0 1.4<γ12<1.9)

Fig.5

θ shows no preference (paucity at small values will be artificial)

β12,γ12 in B+B similar to β13,γ13 in B+B+B,B+T+B

β12,γ12 in B+B+B are different

91

Fig.7

esmax smaller than ep

max (could be seeing or pixel size effects on the secondary

bars)

High percentage of Seyfert nuclei among B+B (46% compared with a few % in disk

galaxies) (consistent with Bars-in-bars scenario for nuclear activity)

92

Friedli & Martinet model : consistent with β-γ relation (Fig.6), but primary bar is

too round (Fig.7) (probably because poorer spatial resolution at large radii in their

simulation)

93

◆ Friedli et al. (1996, A&AS, 118, 461)

JHK photometry of 13 galaxies from Wozniak et al (1995,AAS,111,115)

Same analysis as Wozniak et al.

94

- Results are similar to I-band results exceptγ tend to be smaller for K band (Fig.3)

probably because K better traces stellar mass

- θ is distributed evenly (deprojection does not change the result)

95

Hubble type dependence

- θ shows no dependence

- β andγ larger for late types (for γ, probably because of bulge effect)

- esmax shows no dependence

- epmax probably larger for late-types

96

Numerical model

1) Bno : mass ratios = disk 0.5, bulge 0.05, gas 0.055

2) Bsf : same as Bno but includes star formation

Two models evolve qualitatively similar.

Primary bar forms gas inflow secondary bar forms in the center

Two bars rotate with different pattern speeds

◆ Laine, Shlosman, Knapen, & Peletier (2002,ApJ,567,97)

Theoretically motivated by Shlosman et al. (1989, Nature, 338, 45 )

1) Seyfert sample (56): vhel < 6000 kms-1 HST/NICMOS F160W(H) images

+ a few well-known Seyferts

R>0.45 (RC3)

2) Control sample (56): similar distribution to Seyfert sample in

- absolute B magnitude

- distance

- axis ratio (R)

- morphological type

Analysis:

NICMOS(H-band) + 2MASS(H-band) [5”-30”] + DSS (optical)[30”-]

- ellipse fit (IRAF/GALPHOT)

- deprojection (assuming galaxy outer parts are flat and circular)

Bar detection:

1) ellipticity (1-b/a) rise and fall by >0.1

2) position angle constant (<20°)

Bar length ≡ radius where ellipticity peaks

Bar ellipticity ≡ maximum ellipticity

Results:

1) critical length = 0.06 ×D25 or 1.6 Kpc ( Fig.3 Fig.4)

Fig.7 (secondary bar length ⇔ ILR)

2) Twists are predominant in late-type spirals (Fig.5)

97

98

99

◆Erwin & Sparke (2002, AJ, 124,65)

Motivation: Past observational study compared incidence of double bars in Seyfert

and normal galaxies. But no complete sample was used.

This study = survey of a complete sample of early-type optically barred galaxies

Sample: barred (after RC2) S0-Sa galaxies from UGC

δ>-10°, vhel< 2000 km/s, D25>2’, axial ratio a/b <2

Virgo cluster galaxies excluded to avoid possible environmental effects

38 galaxies (20 S0, 10 S0/a, 8 Sa) (25 SB, 13 SAB)

Imaging in B and R bands (WYIN telescope)

Archival HST data (WFPC2 with F606W, F814W, NICMOS with F160W)

Analysis:

Stellar structures: secondary bars, inner disks, stellar nuclear rings

Gaseous structures: dusty and star-forming nuclear rings, nuclear spirals,

off-plane dust structures (small polar rings, inclined dust

disks)

Detection: ellipse fit to R band, F814W, F160W images candidate features was

examined by unsharp masking and color maps (Fig.2) discriminate between bars,

rings, spirals (can have similar ellipse-fit features)

100

101

Result: (Table2)

- at least 1/4 of galaxies have inner bars (in all Hubble types)

- inner stellar disks are more common in earlier types

- dusty/star-forming rings and nuclear spirals are more common in late types

- none of these features show any preference for bar strength (SB or SAB)

- off-plane gas are most common in S0

Fig.3

102

Angle between outer and inner bars (Fig.3) no significant preference for either

leading or trailing two bars rotate independently

Sizes of inner structures (Fig.4)

Inner bars have 0.05 – 0.14 primary bar length (240-1000pc)

bar length ratio in simulation : 0.26-0.5 (Friedli & Martinet), 0.21 (Friedli et

al. 1996), 0.15 (Rautiainen & Salo 1999)

Ellipticity: smaller than primary bars (Fig.6) (intrinsic roundness and/or bulge

contamination)

Inner disks have a wider size distribution (Fig.4)

nuclear ring:

- dusty/star-forming rings in late types

- Stellar rings in S0 (evolved from star-forming ring / or product of double bar

forcing) (the latter scenario cannot explain two stellar rings without inner bar in

the sample)

- Co-existence with inner bar: 6 out of 10 double barred galaxies (vs. only 27% in

single bar galaxies) For these galaxies, inner bar length is only a bit smaller

than ring sizes

consistent with [inner bar’s CR = outer bar’s ILR]-hypothesis because nuclear

rings are believed to mark ILR

[inner bars do not require nuclear rings]

103

104

Nuclear activity:

31 galaxies have classification in the literature

- AGN and HII nuclei incidences agree with Ho et al.

- inner bar / inner disks do not influence nuclear activity

- AGN activity is closely related to nuclear dusty/star-forming ring, nuclear spirals,

off-plane dust

- SAB may have a higher AGN incidence than SB

§6 High-z Bars: Cosmological Perspectives

fundamental questions: When and How did barred galaxies form?

Observations of distant galaxies (with large look-back times)

6.1 Observations

◆ Abraham et al.(1999, MN, 308, 569)

46 WFPC2-imaged galaxies (in HDF) in F814W (I-band)

rest-frame optical bar fraction decreases from 24% at z ～ 0.2-0.7 to 5% at z >0.7

Estimate of Bar Strength (using two isophotes)

1) pixels with > 1.5 σ above sky level are used.

2) 1% and 85% of the maximum flux level used to define outer and inner regions.

3) calculate second order moments

4) calculate (b/a)outer and (b/a)inner and PA difference φ.

5) correction for inclination i = cos-1[(b/a)outer ] →(b/a)2

1)Test for z ～ 0

Frei et al. Sample (1996) (Fig.1)

For inclination < 60°‘(b/a)2=0.5’ effectively distinguish between barred and

unbarred galaxies.

2) Test for HDF condition

- Frei et al. Sample redshifted artificially to 0<z<1.5 to determine the faintest

magnitude to which (b/a)2 can be determined accurately. →I814W = 23.2

- Bright HDF galaxies degraded to the magnitude limit (Fig.2)

105

106

Analysis of HDF Sample:

I band images

z <1 to avoid band shift effect and retain high S/N

Spiral galaxies are extracted using A and C (see Appendix)(and i < 60°)

→ 20 HDF-N and 26 HDF-S spirals

→ 9 HDF-N and 13 HDF-S spirals are strongly barred (48%)

[Caveat: Barred galaxies may have been preferentially excluded in extracting spiral

galaxies using A and C]

All galaxies in HDF-S/N to I814W = 23.2 checked.

→ Visual classification and A-C spiral selectin are consistent.

Results:

Fig.4 Bar fraction decreases as z increases

[Caveat: Unbarred galaxies are intrinsically more luminous than barred

galaxies so that high-z sample is dominated by unbarred galaxies]

→ Local (z ～ 0) galaxy catalogues (e.g., RC3, Revised Shapley-Ames Catalog) do

not support this.

SBc are slightly less luminous than SAc (van den Bergh 1998, conference

proceedings)

107

Interpretations:

1) High-z disks are not massive enough to be bar-unstable.

2) High-z disks have large random motions and cannot create bars.

3) Bars are more efficiently destroyed at higher z (e.g., by galaxy mergers,

especially minor mergers which turn barred spirals into unbarred spirals)

4) Buckling Instability or Central Mass Growth turns bars into bulges so that

we see few bars at redshift proved in this study.

[3), 4) need second bar generation to explain high bar incidence at z ～ 0]

Appendix: C & A (Abraham et al., 1994, ApJ, 432, 75)

A = area enclosed by the isophote at a given (typically 2σ) level above the sky

Mxx ≡ (i,j)∈A

x2Iij / (i,j)∈A

Iij , Mxy ≡

(i,j)∈A

xyIij /

(i,j)∈A

Iij

Myy ≡ (i,j)∈A

y2Iij / (i,j)∈A

Iij

Define `normalized radius' by

r2 = Mxx x2 + Myy y2 - 2 Mxy xy , so that E(1)=A.

Define `concentration parameter C' by

C ≡ (i,j)∈E(α)

Iij /

(i,j)∈E(1)

Iij

where α is the 'shrinking factor'(usually α=0.3).

Define `asymmetry parameter A' (Abraham et al. 1996, ApJS, 107, 1)

Rotate Iij by 180° about center Jij

A ≡ 1

2 (i,j)∈A

(Iij-Jij) /

(i,j)∈A

Iij

A-C diagram (Abraham et al. 1996, MN, 279, L47) can separate galaxy morphology

(Fig.1, visual morphology by Richard Ellis)

108

◆ Sheth et al. (2003, ApJ, 592, L13)}

HDFN NICMOS (H-band 1.6 μm) to examine effects of

1) Bandshifting

2) Limited spatial resolution

Bandshifting

NICMOS data provide rest-frame V through I-band images for z > 0.7.

Important because

1) Bars are composed of old populations

2) Bars often have non-uniform dust obscuration and peculiar star formation

(→ Fig.1)

109

Analysis:

1) 904 galaxies with photometric or spectroscopic redshift in HDFN

(206 at z<0.7, 226 at 0.7<z<1.1, 472 at 1.1<z)

2) 136 candidate disk galaxies selected using V, I, H images

(41 at z<0.7, 95 at 0.7<z)

3) IRAF ELLIPSE routine applied to identify bars

(= constant position angle and increasing ellipticity)

Bar will be missed if

- the galaxy is highly inclined

- bar position angle is the same as the disk

- underlying disk is too faint

- data have poor resolution

Fraction of barred galaxies will not be overestimated

Results:

- For z<0.7: 5 barred spirals + 2 candidates

consistent with Abraham et al. (1999) (7 barred spirals for z<0.7)

- For z>0.7: 4 barred spirals (Fig. 2, Table 1) + 5 candidates

Abraham et al. (1999) 2 barred spirals for z>0.5

More barred galaxies despite more conservative bar identification than

Abraham et al.(‘ellipse fitting over entire image’ vs ‘only two isophote’)

110

Introduce cutoff at I(AB)=23.7 (same as Abraham et al. )

For z>0.7: 3 barred galaxies among 31 disk galaxies

consistent with bar fraction not decreasing at z>0.7

Spatial Resolution and Visibility of Bars

Typical bar size in nearby galaxies ～5 kpc

NICMOS bars are larger than 12 kpc

Bar fraction (> 12 kpc):

- 4/95 for z>0.7

- 3/31 for z>0.7 (for I(AB)<23.7 as in Abraham et al.)

higher than the local value 1/44 (SONG)

[SONG = Survey Of Nearby Galaxies (Regan et al. 2001, ApJ, 561, 218)

44 Sa-Sd galaxies brighter than 11.0 B-mag, with V < 2000 kms-1

and i < 70°(originally selected for BIMA CO survey)]

Implications:

1) Massive disks were already present 7 Gyr ago.

consistent with star formation history

2) Interactions induced bars

◆ Elmegreen, Elmegreen & Hirst (2004, ApJ, 612, 191)

ACS F814W imaging of Tad-pole galaxy field (3.9' × 4.2')

186 galaxies with major axis larger than 0.5”(= 10 pixels)

bar detection :

1) visual detection + (a maximum ellipticity accompanied by a change in

position angle at the same radius) → 'clearly barred'

2) twist of isophote in center → 'inner isophotal twist'

dependence of bar fraction on inclination and size taken into account

(i.e., bar fraction decreases in highly inclined or small galaxies)

Results: constant bar fraction (20-40%) at z ～ 0 - 1.1

111

◆ Jogee et al. (2004, ApJ, 615, L105)

Abstract

1) 'How bars evolve over cosmological times' has yet to be addressed.

- a recent phenomenon or abundant at early cosmological epochs?

- short-lived or long-lived?

- recurrent (dissolve and re-form) or one-time event?

- stellar bars ⇔ hierarchical clustering of galaxy evolution, underlying disk

evolution ?

2) investigate frequency of bars out to z ～ 1 using 1590 galaxies from GEMS.

- two color images from HST ACS (Advanced Camera for Surveys)

- redshifts from COMBO-17

3) results:

constant bar fraction (～ 30%) at lookback time 2-6 Gyr (z ～0.2-0.7), 6-8 Gyr (z

～ 0.7-1.0), and present.

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4) implication:

- cold gravitationally unstable galactic disks already present at z ～ 1

- bars have a long lifetime

Motivation: limitations of previous studies

1) Abraham et al. (1999, MN, 308, 569) suffers from

- bandshift effects (F814W observe rest-frame ～ 500 nm)

- low resolution of WFPC2 (～ 0.1” in F814W → miss <5kpc bars )

2) Sheth et al (2003, ApJ, 592, L13 =S03)

NICMOS images of 95 galaxies in HDF in F160W (H-band)

- bandshift effects much reduced

- even lower resolution (～ 0.2-0.3” in F160W) than WFPC2

3) Elmegreen, Elmegreen & Hirst (2004, ApJ, 612, 191)

ACS F814W imaging of Tad-pole galaxy field (3.9' × 4.2')

- large (0.1-0.4) error of photometric redshifts (Benitez et al. 2004, ApJS, 150,1)

F475W, F606W, F814W → photo-z

(present study: improved by using COMBO-17 high-accuracy photo-z)

- small sample size precludes absolute magnitude completeness at different z

(overcome by GEMS galaxies)

- bandshift effects (minimized by two passbands)

Observations, Sample, Methodology

GEMS (Rix et al. 2004, ApJS, 152, 163)

・ two-color (F606W, F850LP) HST ACS imaging survey

・ 28' × 28' field centered on Chandra Deep Field South

・ high resolution ～ 0.05” (360pc at z ～ 0.7)

・～ 8300 galaxies at z ～ 0.2 - 1.1

・ redshift & SED available from COMBO-17 (Wolf et al. 2004)

This paper: ～ 25% of GEMS (14' × 14' ～ 30 ×HDF )

1590 galaxies at z ～ 0.2 - 1.0 and RVega <24

Method: ellipse fitting

・ 90% of 1590 (1430) galaxies successfully fitted.

・ 10% failure = disturbed systems or low surface brightness objects

113

・ inclined system (i > 60°) excluded.

Selecting disk galaxies: (大規模サンプルで銀河の形態分類をどうするか?)

(1) Sersic n < 2.5 (Bell et al. 2004, ApJ, 600, L11)

GEMS F850LP images of 1492 0.65 < z < 0.75 galaxies (～ rest-frame V-band)

morphology classification:

1) by eye → E/S0, Sa, Sb-Sdm, Peculiar/Strong Interaction, Irregular/Weak

Interaction, unclassifiable

2) automated galaxy classification using single Sersic model

n = 2.5 separates early (E/S0) and late (Sb-Sdm) galaxies

(with less than 25% contamination)

('n<2.5-criterion' also tested by using artificial galaxies)

(2) Concentration index C < 3.4 (Conselice et al., 2000, ApJ, 529, 886)

113 nearby galaxies from Frei et al (1996, AJ, 111,1) catalog

aperture photometry (using circular aperture)

C ≡ 5 log [r(80%)/r(20%)] (r1/4 law →C = 5.2, exponential law →C = 2.7)

C vs RC3 morphology

(3) rest-frame U-V < 0.8

- Coleman et al. (1980, ApJS, 43, 393)

SED of local ～ 10 spirals

- Bell et al. (2004) study of GEMS z ～ 0.7

galaxies visually classified Sa-Sm galaxies have U-V < 0.8

Bar detection: (bar の客観的定義が必要)

(1) ellipticity (e) rises to global maximum emax > 0.25,

while PA has a plateau (within ± 20° )

(2) Beyond bar end, e must drop by >0.1, while PA changes by >10°

bar fraction fopt ≡ Nbar/Nsp-disk

Results :

Fig2

- most bars identified have e>0.4, a=0.15”-2.2” (a=1.2-13kpc)

- e<0.3 bars difficult to identify

114

hereafter we discuss only e>0.4 bars

Table 1

- bar fraction constant at ～ 30% ± 6%

- no incompleteness effect

similar bar fractions for

<-18.5 (to match OSU sample with absolute mag. range of -18.5 ～ -23.0)

and

<-19.5 (complete out to z ～ 1.0)

- bar fraction slightly higher in rest-frame I-band than B-band

Redshift dependence

1) agree with Elmegreen et al. (2004, ApJ, 612, 191) about Tad-pole galaxy field

2) do not agree with Abraham et al.(1999, MN, 308, 569)

‘dramatic decline in bar fraction’

115

reasons:

- small bars (a < 0.5”) missed by wider PSF in WFPC2 and NICMOS

- low number statistics

- cosmic variance

- methodology

Comparison with local Universe:

OSU sample (Ohio State University Bright Spiral Galaxy Survey)

(Eskridge et al. 2002)

- fopt ～ 37% based on RC3 'SB' bar class}

- fopt ～ 33% according to B-band ellipse fit (e > 0.4)}

Conclusion:

strong bar (e > 0.4) fraction remains similar at 30 - 37% for

- z ～ 0.7-1.0 (lookback time ～ 6-8 Gyr)

- z ～ 0.2-0.7 (lookback time ～ 2-6 Gyr)

- present day

Implications:

(1) dynamically cold disks already in place by z ～ 1 (バー不安定でバー

ができるための条件)

(2) triaxial and centrally-concentrated DM halos (predicted by CDM

cosmology) not prevalent at z ～ 1

triaxial and centrally-concentrated halo destroy bar

116

(El-Zant & Shlosman, 2002, ApJ, 577, 626)

(3) large-scale stellar bars are long-lived

(4) bar ellipticity and length can evolve

Appendix:

COMBO-17 (=Classifying Objects by Medium-Band Observations in 17 Filters)

(Wolf et al. 2003, A&A, 401, 73; Wolf et al. 2004, A&A, 421, 913)

・ deep surveys of 4 field (34' × 33' each)

・ 17 passbands : 350 nm < λ < 930 nm to obtain SED and photo-z

・ telescope: MPG/ESO 2.2m-telescope on La Silla, Chile

・ complete to mR ～ 24

・ redshift accuracy:

δz/(1+z) ～ 0.02 for R ～ 22

δz/(1+z) ～ 0.1 for R > 24

6.2 Theory

Cosmological N-body simulations

Initial density perturbations formation of dark matter haloes with gas

hierarchical merging of halos galaxies of various mass and size form

Disk galaxies do not form! (angular momentum catastrophe)

Cosmologically motivated numerical simulations for barred galaxies

◆Bournaud & Combes (2002, AA, 392, 83)

Effects of gas accretion and repeated bar instability

Initial disk: stars + gas particles (Q=1.5)

Accretion: increases number of gas particles

2D models: halo and bulge = fixed gravitational potential

parameters Mb/Mdisk,i Mh/Mdisk,i

117

Gas accretion

- Velocity = circular velocity at the outer disk + random motion with Q=1.5

- Position = outer disk edge (azimuthally uniform)

(outer disk edge moves as the accretion proceeds)

- Rate = double the disk mass in 7-10 Gyr

Halo mass partly reduced (e.g. Mh,dot= -1/3 Macc,dot)

Results:

- Generally once formed bar disappear as a result of gas accumulation at the center

in absence of gas accretion (Fig.1)

- gas accretion help maintain a bar or

- gas accretion induces reappearance of bars (Fig.1,Fig.4)

depending upon halo/bulge/disk mass ratios (Fig.3)

- initial gas/star ratio in disk does not affect evolution much , and effect of

gas accretion is more important.

[Fig.4: Fourier analysis Bar strength = max of (tangential force of m=2

component)/(radial force)]

Mechanisms:

Gas accretion favor bar because it increases disk mass.

Bar pattern speed increases.

(Because accretion increases central mass and supply angular momentum)

Ωp increases faster than (inner mass)1/2 ≑ Ω

Rco decreases with time

(Rco/Rdisk decreases also, because Rdisk itself increases by gas accretion)

118

119

Out-of-plane accretion (3D models)

inclined accretion onto a small region of the disk

Results:

- qualitatively the same as 2D

- stronger bar than 2D (because accretion itself introduces non-axisymmetry)

120

◆ Berentzen et al. (2004,MN,347,220)

Once formed bars generally weaken spontaneously or disappear by gas inflow.

But we see many barred galaxies in nearby universe.

How to regenerate bars?

One Possibility = Tidal interaction

Host galaxy ( = disk + halo, both active) in which the first spontaneous bar has

disappeared is perturbed by a companion ( = a rigid Plummer sphere).

1) Host galaxy models are bar-unstable and form bars.

These bars weakened (but not completely vanished) Isolated model I0

2) The final state of this model was run with gas replaced by stars

Weak steady bar lasts for a long time Isolated model I1

Interaction = planar, prograde passage. At the closest passage, the weak bar points

toward the companion.

Results:

- All the interaction models failed to regenerate a bar in I0 (model including gas disk)

- Sufficiently strong interractions regenerated a long-lasting bar in I1 (purely stellar

disk)

Reason: Gas accumulates to the center in I0, which inhibits bar formation.

(Also, angular momentum decrease due to interaction is small in I0)

Implications: Tidally regenerated bars will explain some of high-z and local bars

◆ Immeli et al. (2004,AA,413,547)

Galaxy collapse simulations including dissipative gas and star formation

- Galaxy starts as a (gas+dark matter) sphere( dark matter makes a static potential)

- Gas enters simulation volume at |z|=15 kpc with centrifugally balanced state

and a infall rate of 120 solar mass/yr for initial 1 Gyr

(Gas modeled as an ensemble of inelastically colliding clouds)

Dependence on dissipation efficiency:

121

- Strong dissipation model rapid build-up of disk clump formation in early

gas-rich disk clumps merge and fall to center (‘bulge’ formation)

Star formation rate is high, and attains a peak at bugle formation epoch

- Weak dissipation model disk settles slowly bar instability in largely stellar

disk in late epoch bar becomes shorter and pattern speed increases (because of

mass accretion to center) (bar always ends at co-rotation)

Paucity of high-redshift barred galaxies (Abraham & Merrifield) may be explained,

Because model bar takes a long time before it appears, and once formed it weakens

by the gas accumulation to the center.

Star formation rate is low, and attains the second peak when bar induces gas inflow

to the center. (First peak = disk formation)