Dynamics of Galaxies Bars

1
Dynamics of GalaxiesBars AGN fueling

• Françoise Combes
• Observatoire de Paris

2
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 Stochas
tic Global Percentage SA 15 7 32 Isolated S
AB 7 16 70 SB 4 11 73 SA 3 4 57 Bi
naries SAB 1 16 94 SB 1 11 92 SA 15
32 68 Group SAB 21 38 64 SB 12 45 79
3
N2442
N613
N3351
N5850
4
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

5
Bar Formation
Bars are density waves, and can be considered as
the combination of leading trailing wave
paquets They are more stationnary than spirals
(no torque, if purely stellar) ? quasi mode The
first numerical N-body simulations (Hohl
1971, Miller et al 1970) do not show spirals, but
only bars robust over a Hubble time, since only
made of stars, dissipationless
6
Orbits in a barred potential
Bisymmetric m2 (Fourier component) In the
rotating frame, at the bar pattern speed Ob F eq
F (r, ?, z) - Ob2 r2/2 Integral of motion
(Jacobian) Energy in this referential frame
EJ v2/2 F (r, ?, z) - Ob2
r2/2 Lz not conserved of course, since potential
is non-axisymmetric ? torques
7
Shape of the equivalent potential, in the
rotating frame Bar parallel to Ox Lagrange
points stationnary points L4 L5 maxima, L1
L2 saddle points (max in x, min in y) Around
corotation
The orbits have been computed precisely (cf
Contopoulos Papayannopoulos 1980)
8
Orbit families
The 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, // bar with secondary lobes (4)
at CR, around L4 and L5, stable orbits (5)
after CR, again orbits change orientation (quasi
circular, however)
9
When getting near CR, resonances of higher level
Families x1 et x2
After corotation
Contopoulos Papayannopoulos 1980
10
Obvioulsy x1 orbits support the bar, while X2
orbits weaken it, and can even destroy it
Auto-regulation
The presence of ILR triggers the processus The
orbits no longer support the Bar, beyond
corotation A bar ends in general at a
radius just inner its corotation ? excellent
diagnostic to determine Ob
11
N-body simulations bars
Analytic calculations, based on density wave
theory WKB ? tightly wound waves At 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 density At each dt, one
computes the TF of the density, then
multiplies in Fourier space, the FT(1/r) and the
FT(?) gt inverse FT Softening 1/(r2 a2),
to avoid 2-body relaxation ? gives an idea of the
spatial resolution
12
Methods Tree-code
Approx monopole quadrupole, according opening
criterion Advantage no grid Variable
resolution
Barnes Hut (83)
13
Methods collisions or SPH
For 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
14
Technique SPH convolution
With W( r ) normalised to 1, and finite support
Evaluation of all quantity
Or derivative
Symmetrisation of pressure terms
15
Bar formation
stars
gas
16
Total time 1.2 Gyr
Formation of rings at resonances
17
Formation of a bar
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Bar pattern speed

• The bar pattern speed is such that the bar
  radius lt 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 friction effects on
the halo Debattista Sellwood (1999) Since bars
are rotating fast, the centre of galaxies is not
dominated by DM
19
Vertical profile peanuts
Resonance in z (Combes Sanders 81 Combes et al
90)
The bar in the vertical direction always
develops a "peanut" after a few Gyr Box shape in
the other orientation
20
NGC 128 The peanut galaxy
COBE, DIRBE Milky Way
21
Peanut bulge formation
22
Periodic orbits in 3D Lindblad resonance in
z explains the formation of peanuts
23
Gas response to a bar potential
The gas tends to follow the periodic orbits But
gas orbits cannot cross, because of collisions,
dissipation ? the gas response rotates gradually
at each resonance spirals

24
Sanders Huntley 1976 The number of windings of
the spiral is related To the number of resonances
According to the nature of the gas, its response
changes in morphology Schock waves, if fluid gas
Athanassoula 1992 bar at 45 The presence of
resonances ILR gt orbits x2 ? shocks
25
Torques exerted by the bar on the gas
Torques change sign at each resonance, and can be
deduced by simple geometrical arguments
The gas inside corotation loses its angular
momentum and inflows Outside CR, on the contrary
the gas accumulates at the OLR
26
Formation of rings
Ob 16km/s/kpc Ob 13km/s/kpc
Ob 10km/s/kpc ILR Combes Gerin 1985
Formation of an outer ring at OLR Schwarz, 1981
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Formation of rings at resonances (Schwarz
1984) Give an idea of Vsound ?low
viscosity Gravity torques from the bar Change
sign At each resonance ? Relative equilibrium

Buta Combes 2000
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Nuclear bars
Phenomenon observed since a long time, but
explained since a few years
NGC 4314
NGC 5850
Erwin 2004 Contours B-V colors
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NGC 5728 DSS CFH Adaptive Optics NIR
Embedded bars can form, like russian dolls Here
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).
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NGC4314 Star formation in the ring around the
nuclear bar
The nuclear bars are mainly visibles in NIR, not
perturbed By extinction
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Decoupling of nuclear bars
The natural evolution of a barred disk, with
gas Accumulation of mass towards the centre,
gravity torques Formation of 2 Lindblad
resonances, that weaken the bar The rotation
curve (O) rises more and more in the centre, and
also the precession rate of elongated orbits (O -
?/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 bars primary secondary Ex CR of
the 2nd ILR of the primary
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Friedli Martinet 93
Respective positions of the ring and the bar
Formation of a secondary bar In the N-body gas
simulations
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Secondary bars
Stars
Gas
t
N body SPH (D. Friedli)
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Bars and double bars
35
Angular velocities compared for the 2 bars
Non linear coupling between two waves O
?/m Maintenance by exchange of energy? ?1, ?2
Product ?1?2 with V grad V Or ? grad F,
etc Beating mb m1 m2 ?b ?1 ?2
36
Amplitude spectrum for the mode m2 (Masset
Tagger 97) 2 O- ? versus r Gives the location
of resonance Lindblad ILR 2 O- ? versus
r OLR at t8 Gyr
Spectrum m4 The curves 4 O- ? versus r 4 O ?
Beating wave m4 Obtained at the right
frequency ?b ?s 31.8 13.9 45.7 km/s/kpc
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density
potential
Bar and spiral at different speeds (Sellwood
Sparke 1988)
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Migrations of stars and gas
Resonant scattering at resonances
Sellwood Binney 2002
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DL exchange without heating
Invariant the Jacobian EJ E- Wp L ? DE Wp
DL DJR (Wp-W)/k DL If steady spiral,
exchange at resonance only In fact, spiral waves
are transient The orbits which are almost
circular will be preferentially scattered
Sellwood Binney 2002
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Chemical evolution with migration
O/H, and O/Fe Thick disk is both a-enriched and
low Z Churning Change in L, without
heating Blurring Increase of epicyclic
amplitude, through heating Gas contributes to
churning, and is also radially driven inwards
Shoenrich Binney 2009
41
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

Bar Spiral
Minchev Famaey 2010
42
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 41 ILR

Minchev et al 2010
43
Migration extent
Time evolution of the L transfer with bar and
4-arm spiral Explains absence of AMR Age
Metallicity Relation AVR relation
Initial position of stars ending in the green
interval after 15 and 30 Rotations Black
almost circular s 5km/s
Minchev et al 2010
44
Barspiral migrations
Overlap of resonances
Minchev et al 2010
45
Active nuclei fueling
Bars are the way to drive the gas towards the
centre To 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?
46
Periodic orbits in a potential in cos 2? The gas
tends to follow these orbits, but rotates
gradually by 90 at each resonance
A) without BH, leading B) with BH, trailing
47
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 orbits limited only by their energy in
the rotating frame F( r ) -1/2 O2 r2 Outside
corotation no more limit (abrupt boundary)
48
Fraction of phase space occupied by x1 orbits
supporting the bar
Surfaces of section for a BH of 3 in mass for a
particule of max distance a) 0.25 a b) 0.65a a
size of the bar
49
Surfaces of section for the orbits in the plane
of the galaxy, for various energies (y, dy/dt)
at the crossing point of Oy, with dx/dt gt
0 The invariant curves of the X1 families
disappear at H-0.3 Hasan et al (1993)
50
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)
51
Role of gas in bar destruction
Gas is driven in by the bar torques The angular
momentum is taken up by the bar wave ? This
destroys the bar negative momentum inside CR,
A2 (Wb-W) The gas AM from CR to center is of the
same order Not only the presence of the Central
Mass Concentration A 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)
52
Role of gravity torques
6 of mass in gas bulge 25 Gas inside 300pc
1 More easy to reform the bar!
4 of mass in gas bulge 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
and in 200pc
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Relation between BH-bulge mass
Mbh 0.2 Mbulge
Blue stellar velocities Green gas
velocities Red disks with masers H2O,
OH.. (Magorrian et al 98, Gebhardt et al 02,
Ferrarese Merritt 01, Tremaine et al 02, Shields
et al 02)
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Scaling SMBH, M-s relation
Mbh 0.2 Mbulge
Gultekin et al 2009
56
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-bul
  ges interactions
• Delayed co-evolution Different time-scales
• Better, since it is difficult to find good
  correlations of AGN and bars, or with
  interactions
• Self-regulated growth
• Feedback mechanisms related to the potential
  well (bulge mass)

57
Several bar episodes in a galaxy disks, with
secondary bars Regulation mechanisms
Gas accretion at each gravitational
instability The BH grows in parallel to the
bulge
58
Co-evolution BH and galaxies
Ratio 1000 since mass loss 50
PLE Pure Luminosity Evolution LDDE
Luminosity-dependent Density Evolution
59
BHAR and SFR versus z
--SFR
__BHAR
Dotted lines are BHAR shifted by 100 in Number
and 20 in Rate
60
BHAR and SFR split for intensity
z1
Total is dominated by low-intensities
Zheng et al 2009
61
BHA and SF not in the same objects
z1
Zheng et al 2009
fbulge-bh 650, frecycle2 ? 1300
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Hierarchical formation of BCG
dry mergers since z1 50 of stars formed at z5
mass assembling after z0.5 De Lucia Blaizot
2007
63
Feedback due to Starburst or AGN
Di Matteo et al 2005
64
Perseus Clusterexample of AGN feedback
Salomé et al 2006
Fabian et al 2003
65
A very early assembly epoch for QSOs
The highest redshift quasar currently known SDSS
11483251 at z6.4 has estimates of the SMBH
mass MBH2-6 x109 Msun (Willott et al 2003,
Barth et al 2003)
As massive as the largest SMBHs today, but when
the Universe was lt1 Gyr old!
66
Fueling processes
?When gravity torques exist, they are the most
efficient One 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, m1 (examples in NUGA
survey, Garcia-Burillo et al 2003) -- impossible
to study the phenomena independently (rigid bars
for instance) since processes are self-regulated
67
Statistics on bar strength
Bars 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
68
Quantification of the accretion rate Block,
Bournaud, Combes, Puerari, Buta 2002
Observed
Doubles the mass in 10 Gyr
No accretion
69
With accretion
Gas accretes by intermittence First it is
confined outside OLR until the bar weakens,
then it can replenish the disk, to make it
unstable again to bar formation
without
70
Cycle of bars
Self-regulated cycle ?Bar forms in a cold
unstable disk ?Bar produces gas inflow, and ?Gas
inflow destroys the bar gas
accretion ?
71
Simulations of gas accretion
? Reformation of bars A 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
evolve And the morphological type might oscillate
Mbul/Mdlt1
Mbul/md gt1
72
Changes of types
73
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 O - ?/2
high precession rate ? existence of ILR, nuclear
rings Late weak bulge, no concentration O -
?/2 low precession rate, the corotation is
farther away in the disk, and even sometimes
outside of the stellar disk ? Leaves the
exponential distribution control the radial
profile (Combes Elmegreen 1993)
74
Bars in late-type galaxies (left) "early"
(right) Stars and gas
Rotation frequencies and precession rates
Radial profiles of bars in the 2 morphological
types (CE 93)
75
Instabilities m1
Excentric asymmetries observed in the light
distribution But also in the HI gas at
21cm Richter Sancisi (1994) more than half of
the sample is strongly asymmetric (among 1700
galaxies) Case of M101, NGC 628.. Sometimes a
companion, but most of the time no
companion Retrograde orbits favor m1 (Zhang
Hohl 1978, Palmer Papaloizou 1990) These
lopsided instabilities far from the centre give
insight on the dark matter
76
Kamphuis et al 1991 M101 Note the
numerous bubbles The arrow points to A
super-bubble, due may be to an interaction
77
NGC 628 (Kamphuis et al 1992) Contours HI at
21cm Large extent of gas Around the optical
galaxy
Spirals and fragmentation far from the optical
disk Stability??
78
Possible Mechanisms
Principal difficulty The differential precession
rate very rapid O - ? near the centre Except
for a purely Keplerien disk, potential in
1/R where O ? m1 eigen mode, but with a
strong self-gravity Physical nature of the
instability Simple description in WKB (Lin Shu
64, Toomre 77)
79
Instability m1 In a quasi keplerian disk Adams,
Ruden Shu 1989
80
Amplification at Corotation Energy and angular
momentum are -- positive outside CR -- negative
inside CR Waves are partially transmitted, and
partially reflected at CR With an evanescent zone
if Q gt 1 The reflected wave, by conservation,
has an increased amplitude If this amplifyer is
coupled to a reflexion at resonances or at
boundaries, there is a WASER, or SWING Location
of returning points Op O ?/m (1 - 1/Q2)1/2
81
For m1, there exists an other amplifyer No need
of Corotation The indirect potential, due to the
off-centring of the central mass F ( r, ?, t)
a ?2 r cos (?t - ?) Force with a long
range The disk behaves like a resonant
cavity With the off-centring permanently
stimulating new waves, trailing The central mass
gains angular momentum, and also the disk Outside
CR (change of referential COM, or BH, the
momentum changes sign)
82
While the growth rate for the SWING is ?
O here ? ltlt O 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
83
Models N body SPH

• Density Waves

M 31
Central 10pc of M31
bande I
s
V
WFPC2 / HST
TIGER / CFHT
84
An m1 keplerian mode?
Pattern speed
face-on
observed
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 gt 3000 rotations
• 4 108 yrs

Linear cuts
85
Evolution on the Hubble sequence
86
Principal parameters on the sequence 1.
Bulge/disk ratio concentration of mass
increasing from 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
matter transformed in stars in the evolution,
which could be dark baryons, under gas form 5.
Winding of arms increasing, meaning a higher
stability in "early" systems (mass concentration,
gas/stars ratio)
87
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 formation which 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
88
The Milky Way
Hurt Benjamin 2008
Georgelin Georgelin 1976

• Gas Star models

89
From Fux (1999) N-body simulationsSPH
Bar similar to DIRBE The center of the bar
wanders
Gas flow asymmetric non-stationary
Transient


3kpc arm is a spiral round the bar Parallelogram
interpreted as leading dust-lanes
90
2MASS stellar counts (Alard 2001)
91
Fits results
Sun