Dynamics of GalaxiesBars & AGN fueling

Françoise Combes

Observatoire de Paris

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Barred Galaxies The majority of galaxies are barred (2/3)About 1/3 have strong bars SB, and 1/3 intermediate (SAB)

Bars are also a way to generate Grand design spiral structure

Environmnt Type Stochastic Global PercentageSA 15 7 32%

Isolated SAB 7 16 70%SB 4 11 73%SA 3 4 57%

Binaries SAB 1 16 94%SB 1 11 92%SA 15 32 68%

Group SAB 21 38 64%SB 12 45 79%

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N2442

N613

N3351

N5850

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Spiral Galaxies should be viewed as accretion disks

Galaxies disks in perpetual evolution/ reformation Tend to concentrate mass (tend to a least energy state)

Gravity is the principal engine

But rotation prevents mass to concentrate more Angular momentum should flow away

•Energy dissipation (gas) reduces random motions, but viscous torques insufficient

•Formation of spirals and bars to get rid of angular momentum

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Bar Formation

Bars are density waves, and can be consideredas the combination of leading & trailing wave paquets

They are more stationnary than spirals (no torque, ifpurely stellar) quasi mode

The first numerical N-body simulations (Hohl 1971,Miller et al 1970)do not show spirals, but only barsrobust over a Hubble time,since only made of stars, dissipationless

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Orbits in a barred potential

Bisymmetric m=2 (Fourier component)

In the rotating frame, at the bar pattern speed Ωb

Φ eq = Φ (r, θ, z) - Ωb2 r2/2

Integral of motion (Jacobian)Energy in this referential frame: EJ = v2/2 + Φ (r, θ, z) - Ωb

2 r2/2

Lz not conserved of course, since potential isnon-axisymmetric torques

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Shape of the equivalentpotential, in the rotatingframeBar parallel to Ox

Lagrange points: stationnary pointsL4 & L5 maxima, L1 & L2 saddle points (max in x, min in y)

Around corotation

The orbits have been computed precisely(cf Contopoulos & Papayannopoulos 1980)

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Orbit familiesThe periodic orbits are the squeleton; they attract and trap all other orbits (except chaotic orbits)

(1) Very near the centre, orbits are // bar, family x1(there exists also retrograde orbits x4, low population)

(2) Between the two ILR, if they exist, are the orbits of family x2,perpendicular to the bar, direct and stable (also x3 unstable)x2 disappears if the bar strength is too large (ILR suppressed)

(3) between ILR and corotation, again family x1, // barwith secondary lobes(4) at CR, around L4 and L5, stable orbits

(5) after CR, again orbits change orientation (quasi circular, however)

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Families x1 et x2 After corotation

When getting near CR, resonances ofhigher level

Contopoulos & Papayannopoulos 1980

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Obvioulsy x1 orbits support the bar, whileX2 orbits weaken it, and can even destroy it

Auto-regulation

The presence of ILR triggers theprocessus

The orbits no longer support theBar, beyond corotation

A bar ends in general at a radiusjust inner its corotation

excellent diagnostic to determine Ωb

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N-body simulations: bars

Analytic calculations, based on density wave theoryWKB tightly wound wavesAt the opposite of bars!

Surprise of the 1st numerical simulations (1970)

Self-gravity, collective effects, interactions in N2

N = 1011

Clues: fast Fourier Transforms FFT The potential is the convolution of 1/r by the densityAt each dt, one computes the TF of the density, then multipliesin Fourier space, the FT(1/r) and the FT(ρ) ==> inverse FT

Softening 1/(r2 + a2), to avoid 2-body relaxation gives an idea of the spatial resolution

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Methods: Tree-code

Approx: monopole +quadrupole, according opening criterion

Advantage: no grid Variable resolution

Barnes &Hut (83)

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Methods: collisions or SPHFor gas hydrodynamics, the essential is a weak dissipation

Collisions between particules ("sticky-particules")or finite differences (fluid code)

Or variable spatial resolution: SPH"Smoothed Particules Hydrodynamics" (Lucy & Monaghan 77)

Principle: kernel function(or weight W( r ))with a variable size, which contains a fixed number of neighbors

Density is computed by averaging over neigbors (30-50)

And all other quantities & derivatives similarly

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With W( r ) normalised to 1, and finite support

Evaluation of all quantity:

Symmetrisation of pressure terms

Technique SPH convolution

Or derivative

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Bar formation

stars

gas

16Formation of rings at resonances

Total time: 1.2 Gyr

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Formation of a bar

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Bar pattern speed

The bar pattern speed is such that the bar radius < corotation

During its growth, the bar slows down•The transient stellar spiral arms take away angular momentum•The bar grows, the orbits are more elongated•The equivalent precession is lower

This neglects the dynamical frictioneffects on the halo

Debattista & Sellwood (1999)Since bars are rotating fast, the centreof galaxies is not dominated by DM

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Vertical profile: peanuts

The bar in the vertical direction always develops a "peanut"after a few GyrBox shape in the other orientation

Resonance in z(Combes & Sanders 81Combes et al 90)

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NGC 128The peanut galaxy

COBE, DIRBE Milky Way

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Peanut bulge formation

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Periodic orbits in 3D: Lindblad resonance in zexplains the formation of peanuts

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Gas response to a bar potential

The gas tends to follow the periodic orbits

But gas orbits cannot cross, because ofcollisions, dissipation

the gas response rotatesgradually at each resonance

spirals

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Sanders & Huntley 1976The number of windings of the spiral is relatedTo the number of resonances

Athanassoula 1992

bar at 45°The presence of resonancesILR ==> orbits x2 shocks

According to the nature of the gas, its response changes in morphologySchock waves, if fluid gas

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Torques exerted by the bar on the gasTorques change sign at each resonance, and can be deducedby simple geometrical arguments

The gas inside corotation loses its angular momentum and inflowsOutside CR, on the contrary the gas accumulates at the OLR

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Formation of rings

Ωb = 16km/s/kpc Ωb = 13km/s/kpc Ωb = 10km/s/kpcILR Combes & Gerin 1985

Formation of an outer ringat OLRSchwarz, 1981

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Buta & Combes 2000

Formation of rings at resonances(Schwarz 1984)

Give an idea of Vsoundlow viscosity

Gravity torques from the barChange signAt each resonance

Relative equilibrium

N1433

N3081

N6300

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Nuclear barsPhenomenon observed since a long time, but explained since a few years

NGC 4314

Erwin 2004Contours + B-V colors

NGC 5850

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Embedded bars can form, like russian dollsHere a nuclear bar (at right, field of 36")inside the primary bar (at left, field of 108").

Note the star above the nuclear bar, giving the scale The secondary bar rotates faster than the primary (Combes et al. 2001).

NGC 5728DSS+CFHAdaptive OpticsNIR

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NGC4314

Star formation in the ringaround the nuclear bar

The nuclear bars are mainly visibles in NIR, not perturbedBy extinction

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Decoupling of nuclear bars

The natural evolution of a barred disk, with gasAccumulation of mass towards the centre, gravity torques

Formation of 2 Lindblad resonances, that weaken the bar

The rotation curve (Ω) rises more and more in the centre, and alsothe precession rate of elongated orbits (Ω - κ/2)

The central matter can no longer follow the rest of the disk decoupling

To avoid the chaos, there is a common resonance between the 2 barsprimary & secondaryEx: CR of the 2nd = ILR of the primary

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Formation of a secondary barIn the N-body + gas simulations

Friedli &Martinet 93

Respectivepositions of the ringand the bar

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Secondary bars

N body + SPH (D. Friedli)

Stars

Gas

t

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Bars and double bars

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Angular velocitiescompared for the 2 bars

Non linear coupling between two waves Ω= ω/m

Maintenance by exchange of energy? ω1, ω2

Product ξ1ξ2* with V grad V

Or ρ grad Φ, etc…

Beating mb = m1 + m2

ωb = ω1+ ω2

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Amplitude spectrum for the modem=2 (Masset & Tagger 97)

2 Ω- κ versus rGives the location of resonance Lindblad ILR2 Ω- κ versus rOLRat t=8 Gyr

Spectrum m=4The curves 4 Ω- κ versus r4 Ω+ κ

Beating wave m=4Obtained at the right frequencyωb + ωs

31.8 + 13.9 =45.7 km/s/kpc

37Bar and spiral at different speeds (Sellwood & Sparke 1988)

density potential

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Migrations of stars and gas Resonant scattering at resonances

Sellwood & Binney 2002

All stars with small epicycles

LCR

ILR OLR

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L exchange without heating

Sellwood & Binney 2002

Invariant: the JacobianEJ= E- p L E = p L

JR = (p-)/ L

If steady spiral, exchange at resonance only

In fact, spiral waves are transient

The orbits which are almost circular will be preferentially scattered

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Chemical evolution with migration

Shoenrich & Binney 2009

O/H, and O/FeThick disk is both -enriched and low Z

Churning = Change in L, without heatingBlurring= Increase of epicyclic amplitude, through heating

Gas contributes to churning, and is also radially driven inwards

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Transfert of L, and migrations Bars and spirals can tranfer L at Corotation

Transfer multiplied if several patterns with resonances in common

Much accelerated migrations

Minchev & Famaey 2010

Bar Spiral

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Effect of coupled patterns Time evolution of the L transfer with bar and 4-arm spiral, in the MW

Top: spiral CR at the Sun

Bottom: near 4:1 ILR

Minchev et al 2010

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Migration extentTime evolution of the L transfer with bar and 4-arm spiral

Explains absence of AMR Age Metallicity Relation+AVR relation

Initial positionof stars ending in thegreen intervalafter 15 and 30 Rotations

Black: almost circular = 5km/s

Minchev et al 2010

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Bar+spiral migrationsOverlap of resonances

Minchev et al 2010

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Active nuclei fueling

Bars are the way to drive the gas towards the centreTo fuel starbursts, but also AGN

Yet, in a first step, matter is trapped in resonant rings at ILR

The secondary bar allows to go farther, and takes over

What are the orbits inside the secondary bar ?

Nuclear spiral? Third bar?How many resonances?

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Periodic orbits in a potential in cos 2θThe gas tends to follow these orbits, but rotates gradually by 90° at each resonance

A) without BH, leading

B) with BH,trailing

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Destruction of bars

Bars self-destroy, by driving mass towards the centre (gas)

With a central concentration of mass(concentrated nuclear disk, black hole)Less and less regular x1 orbits, more and more chaotic orbits,deflection due to the central mass

Evolution: destruction of periodic orbits, if rapid evolution And radial shift of resonances

Creation of "lenses", diffusion of chaotic orbitslimited only by their energy in the rotating frameΦ( r ) -1/2 Ω2 r2

Outside corotation: no more limit (abrupt boundary)

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Fraction of phase space occupied by x1 orbits supporting the bar

Surfaces of section for a BHof 3% in mass

for a particule of max distancea) 0.25 ab) 0.65aa = size of the bar

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Surfaces of section for theorbits in the plane of thegalaxy, for various energies

(y, dy/dt) at the crossing point of Oy, with dx/dt > 0

The invariant curves of the X1 families disappear at H~-0.3Hasan et al (1993)

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Formation of lenses, and of "ansae" During the destruction of the bar

The first orbits to become chaotic are between ILR and CR

Near the central black hole, the potential becomes axisymmetric and regular

The lenses in galaxies can be detected by their radial profile, characteristic and steep (Kormendy 1982)

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Role of gas in bar destruction

Gas is driven in by the bar torquesThe angular momentum is taken up by the bar wave

This destroys the bar negative momentum inside CR, ~ A2 (b-)The gas AM from CR to center is of the same order

Not only the presence of the Central Mass ConcentrationA CMC of only 1% is not sufficient to destroy the bar(Shen & Sellwood 2004, Athanassoula et al 2005,but Hozumi & Hernquist 2005)But 1-2% of gas infall is enough to transform a bar in a lens(Friedli 1994, Berentzen et al 1998, Bournaud & Combes 02, 04)

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Role of gravity torques

6% of mass in gasbulge 25%Gas inside 300pc ~ 1%

More easy to reformthe bar!

4% of mass in gasbulge 20%Gas inside 300pc ~ 0.8%

Bournaud & Combes 2004

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Inflow with two embedded bars

Cumulated gas inflow (70pc)

Inflow rate in 20pc andin 200pc

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Relation between BH-bulge mass

Blue: stellar velocities Green: gas velocitiesRed: disks with masers H2O, OH..(Magorrian et al 98, Gebhardt et al 02, Ferrarese &Merritt 01,Tremaine et al 02, Shields et al 02)

Mbh = 0.2% Mbulge

55Gultekin et al 2009

Scaling SMBH, M- relation

Mbh = 0.2% Mbulge

Invoked mechanisms

Co-evolution: each time gas is driven to the center to form stars, a fraction fuels the BH

Possible, but through secular evolution/pseudo-bulges & interactions

Delayed co-evolution: Different time-scalesBetter, since it is difficult to find good correlations of AGN and bars, or

with interactions

Self-regulated growthFeedback mechanisms: related to the potential well (bulge mass)

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Several bar episodes in agalaxy disks, with secondary bars

Regulation mechanisms

Gas accretion at each gravitational instability

The BH grows in parallelto the bulge

Zheng et al 2009

Co-evolution BH and galaxies

PLE: Pure Luminosity EvolutionLDDE Luminosity-dependent Density Evolution

Ratio 1000since massloss 50%

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BHAR and SFR versus z--SFR

__BHAR

Dotted lines are BHAR shifted by 100 in Number and 20 in Rate

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BHAR and SFR split for intensity

Total is dominated by low-intensities

z=1

Zheng et al 2009

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BHA and SF not in the same objects

fbulge-bh = 650, frecycle=2 1300

z=1

Zheng et al 2009

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Hierarchical formation of BCG

dry mergers since z=150% of stars formed at z=5; mass assembling after z=0.5De Lucia & Blaizot 2007

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Feedback due to Starburst or AGN

Di Matteo et al 2005

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Perseus Clusterexample of AGN

feedback

Salomé et al 2006

Fabian et al 2003

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A very early assembly epoch for QSOs The highest redshift quasar currently known

SDSS 1148+3251 at z=6.4 has estimates of the SMBH mass

MBH=2-6 x109 Msun (Willott et al 2003, Barth et al 2003)

As massive as the

largest SMBHs today,

but when the Universe

was <1 Gyr old!

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Fueling processes

When gravity torques exist, they are the most efficientOne primary bar, then a secondary bar (more transient) ILR can stop inflow only for a while

-- if not, gravitational instabilities create viscosity

-- or create clumps (unstable disks), very non-axisymmetric flows

-- dynamical friction of GMC against the bulge

-- asymmetries due to a companion, or anisotropic accretion, m=1(examples in NUGA survey, Garcia-Burillo et al 2003)

-- impossible to study the phenomena independently (rigid bars forinstance) since processes are self-regulated

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Statistics on bar strengthBars provoke their own destruction, by driving gas towards the center. After 5 Gyr there should not be any bar left

Why so many bars today? (more than 2/3 of galaxies)Even more in NIR images

Sample of 163 galaxies (OSU, Eskridge et al 2002)

Bar strength estimated by Qb

by Fourier Transforms of the potential (Block et al 2002)also Whyte et al (2002), axis ratio

N

Qb

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Quantification of the accretion rate Block, Bournaud, Combes,

Puerari, Buta 2002

Observed

No accretionDoubles the massin 10 Gyr

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With accretion

Gas accretes by intermittenceFirst it is confined outside OLR until the bar weakens,

then it can replenish the disk, to make it unstable again to bar formation

without

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Cycle of bars

Self-regulated cycle:Bar forms in a cold unstable diskBar produces gas inflow, and Gas inflow destroys the bar +gas accretion

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Simulations of gas accretion Reformation of barsA galaxy is in perpetual evolution, and accretes gas all along its life 3 or 4 bar episodes in the galaxy life-time

The ratio Mbulge/Mdisk and the gas fraction evolveAnd the morphological type might oscillate

Mbul/Md<1

Mbul/md >1

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Changes of types

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Bar pattern speeds vs types

For morphological type "Early": the radial profile is flat

For morphological type "Late": the radial profile is exponential

Early: massive bulge, large central mass concentration Ω - κ/2 high precession rate existence of ILR, nuclear rings

Late: weak bulge, no concentration Ω - κ/2 low precession rate, the corotation is farther awayin the disk, and even sometimes outside of the stellar disk

Leaves the exponential distribution control the radial profile(Combes & Elmegreen 1993)

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Bars in late-type galaxies (left)

& "early" (right)Stars and gas

Rotation frequenciesand precession rates

Radial profiles of barsin the 2 morphological types (CE 93)

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Instabilities m=1

Excentric asymmetries observed in the light distribution But also in the HI gas at 21cmRichter & Sancisi (1994) more than half of the sample is stronglyasymmetric (among 1700 galaxies)

Case of M101, NGC 628.. Sometimes a companion, but most of thetime no companion

Retrograde orbits favor m=1 (Zhang & Hohl 1978,Palmer & Papaloizou 1990)

These lopsided instabilities far from the centre give insight on the dark matter

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Kamphuis et al 1991M101

Note the numerousbubbles

The arrow points toA super-bubble, duemay be to aninteraction

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NGC 628(Kamphuis et al 1992)

Contours = HI at 21cm

Large extent of gasAround the optical galaxy

Spirals and fragmentation far from the optical diskStability??

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Possible Mechanisms

Principal difficulty: The differential precession rate very rapidΩ - κ near the centre

Except for a purely Keplerien disk, potential in 1/Rwhere Ω = κ

m=1 eigen mode, but with a strong self-gravity

Physical nature of the instability

Simple description in WKB (Lin & Shu 64, Toomre 77)

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Instability m=1In a quasi keplerian diskAdams, Ruden & Shu 1989

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Amplification at Corotation

Energy and angular momentum are:-- positive outside CR-- negative inside CR

Waves are partially transmitted, and partially reflected at CRWith an evanescent zone if Q > 1

The reflected wave, by conservation, has an increased amplitude

If this amplifyer is coupled to a reflexion at resonances orat boundaries, there is a WASER, or SWING

Location of returning points

Ωp = Ω + κ/m (1 - 1/Q2)1/2

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For m=1, there exists an other amplifyer

No need of Corotation

The indirect potential, due to the off-centring of the central mass

Φ ( r, θ, t) = α ω2 r cos (ωt - θ)

Force with a long rangeThe disk behaves like a resonant cavityWith the off-centring permanently stimulating new waves,trailing

The central mass gains angular momentum, and also the diskOutside CR(change of referential COM, or BH, the momentum changes sign)

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While the growth rate for the SWING is γ ~ Ωhere γ << Ω

This mode allows the inner disk to lose angular momentum, And to the gas to fall onto the central BH

Applications to oscillations of the nuclear disk, around a central Black hole (cf M31, NGC 3504..)

Most galaxies with a massive bulge possess a central black hole

Relation of Magorrian

MBH = 0.2% M bulge

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Models N body + SPH

• Density Waves

WFPC2 / HST

TIGER / CFHT

M 31

bande I

V

Central 10pcof M31

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An m=1 keplerian mode?Pattern speed

face-on« observed »

Linear cuts

Major-axis Minor-axis

BH: 7 107 Msol

Disk: 20-40% of total mass

Pattern speed: 3 km/s/pc (orbital frequency: 250 km/s/pc)

Life-time: > 3000 rotations ~ 4 108 yrs

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Evolution on the Hubble sequence

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Principal parameters on the sequence:

1. Bulge/disk ratio: concentration of mass increasingfrom Sc to Sa: direction of evolution

2. Total mass increasing from "late" to "early"

3. Fraction of gas decreasing, through star formation

4. Fraction of dark matter decreasing: part of the dark mattertransformed in stars in the evolution, which could be dark baryons, under gas form

5. Winding of arms increasing, meaning a higher stabilityin "early" systems (mass concentration, gas/stars ratio)

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Conclusions

Galaxies are not fixed on a given morphology on the Hubble sequence

Bars appear and disappear, several barred episodes according to the amount of gas accreted

Spiral galaxies have never completed their formationwhich continues all along the Hubble time

Either by internal, secular, evolution

Either by interaction between galaxies, and mergers

Bars drive gas to the center, available to fuel the AGN

The Milky Way

Gas & Star models

Georgelin & Georgelin 1976

Hurt & Benjamin 2008

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From Fux (1999)N-body simulations+SPH

Bar similar to DIRBEThe center of the bar wanders

Gas flow asymmetricnon-stationary

Transient

3kpc arm is a spiralround the bar

Parallelogram interpretedas leading dust-lanes

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2MASS stellar counts (Alard 2001)

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Fits results

Sun