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NGC 5383 NGC 1300 Chapter 11 Barred Galaxies Barred Galaxies

NGC 7741 NGC 1097 Barred Galaxies

Gallery of Barred Spirals Credit: (upper left) Pat Balfour/Adam Block/NOAO/AURA/NSF (upper right) Nicole Bies and Esidro Hernandez/ Combes et al.: Chapter 6 Adam Block/NOAO/AURA/NSF (lower left) Adam Block/NOAO/AURA/NSF (lower right) R. Jay GaBany

3 4 Overview of Barred Galaxies Andromeda

Barred Galaxies Barred Galaxies About 2/3 of spirals are barred 1/2 are strongly barred (SB) 1/2 are intermediately barred (SAB) Nearby barred galaxies: M31 (Andromeda), Magellanic clouds Milky Way is probably barred Isovelocity curves (spectroscopic observations) are distorted to an S-shape under the influence of a bar Smooth, almost constant surface brightness along the major axis of bars Bars can be biaxial or triaxial

Are bars responsible for the spiral structures? Credit: Adam Block & Tim Puckett 5 6 Spirals and Their Environment Theoretical Studies

Barred Galaxies Barred Galaxies

Barred potential. A bar creates a bisymmetric gravitational poten- Environment Type Stochastic Global Spirals Global Spirals (%) tial (Fourier expansion of order m = 2), which rotates at an angular Isolated SA 15 7 32 velocity Ωp. SAB 7 16 70 In cylindrical coordinates (r.φ,z), consider the equivalent potential in a reference frame rotating at Ωp SB 4 11 73 Ω2r2 Binary SA 3 4 57 Φ = Φ(r, φ,z) p . equiv − 2 SAB 1 16 94 The energy of a particle is SB 1 11 92 υ2 Ω2r2 E = + Φ(r, φ,z) p , Grouped SA 15 32 68 J 2 − 2 SAB 21 38 64 and the equation of motion is written as centrifugal force SB 12 45 79 d2r = Φ 2Ω υ + Ω2 r . Total 79 180 69 dt2 −∇ − p × p Coriolis force # $! " ! "# $

7 8 Equivalent Barred Potential Lindblad Resonances

Barred Galaxies Barred Galaxies Recall corotation and Lindblad resonances when introducing the Spiral Structures of Galaxies.

5 Lagrangian points

L3: central minimum

L1, L2: saddle points, unstable

L4, L5: maxima, stable Corotation zone: a ring- shaped region consists of L1, L2, L4, and L5 Carroll & Ostlie Fig. 25.30 9 10 Lindblad Periodic Stellar Orbits (I)

Spiral Structure of Galaxies Barred Galaxies Resonances Close to the center (with low energies) x1 family: direct, elongated orbits parallel to the bar

x4 family: retrograde orbits Whether there is a spiral perturbations with m arms, a Between the two ILRs bar, or a companion, a x2 family: direct, elongated orbits perpendicular to the bar, disappear in privileged angular velocity !p the case of strong bars that rotates with the perturbation often exists in a x3 family: similar to the x2 family but unstable spiral galaxy. Between the outer ILR and the CR

x1 family with secondary lobes at orbital extremities In a reference frame that At the CR rotates with , the stars rotate at !! = ! " !p. Stellar orbits close Stable periodic orbits around L4 and L5 that do not revolve around the up after m lobes if !! = !/m. center Lindblad resonances refer to the case of m=2.

11 12 Periodic Stellar Orbits (II) Periodic Stellar Orbits (III)

Barred Galaxies Barred Galaxies Between CR and OLR Bar Depopulated to the benefit of a ring at the CR, especially for a strong bar of ! shape Far away from CR Nearly circular orbits, perturbations of the bar potential averaged in azimuth into a quasi-axisymmetric potential Retrograde perpendicular orbits are most common, but direct orbits aligned with the bar also exist Irregular (ergodic) orbits mainly found in this region

A bar cannot go beyond the CR ! !p = ! at the end of the bar

Contopoulos & Papayannopoulos 1980, A&A, 92, 33 13 14 Periodic Stellar Orbits (IV) Periodic Stellar Orbits (V)

Barred Galaxies

Bar

Contopoulos & Contopoulos & Papayannopoulos Papayannopoulos 1980, A&A, 92, 33 1980, A&A, 92, 33

15 16 Periodic Stellar Orbits (VI) Periodic Stellar Orbits (VII)

Barred Galaxies Barred Galaxies r = the intersection r retrograde orbits of the orbits with r the x-axis In the case of a strong bar, the x2 family no longer exists. The slower the , the stronger the bar must be to eliminate zero-velocity curve the x2 family.

direct orbits

Contopoulos & Contopoulos & Papayannopoulos Papayannopoulos 1980, A&A, 92, 33 1980, A&A, 92, 33 17 18 Summary of Stellar Orbits Galaxies with Two ILRs (I)

Barred Galaxies Barred Galaxies Periodic orbits

The x1 family: mainly responsible for construction of the bar

The x2 family: tends to weaken and even destroy the bar when is !p small In addition to periodic stellar orbits, ergodic orbits also exist but mainly found beyond the CR

M94 (NGC 4736)

NGC 4313 inner and outer rings Nuclear ring

Credit: Benedict (U. of Texas), inner and outer rings NASA

19 20 Galaxies Numerical Methods

Barred Galaxies Barred Galaxies with Two Cell size adjustment Replace the Cartesian coordinates by cylinderical coordinates Tree code ILRs (II) Adapt the resolution The interaction between nearby particles is treated exactly like summation; the interaction between distant particles, only the first terms of the expansion are retained Smoothed Particle Hydrodynamics (SPH) Model the gas as an ensemble of fluid elements

Benedict, Smith, & Kenney 1996, AJ, 111, 1861 21 22 Simulation Rotation Evolution of Bars

Barred Galaxies Barred Galaxies

Combes & Sanders 1981, A&A, 96, 164

First form a transient spiral, after one galactic rotation, turn into a quasi-stationary The more extended the bar. bar, the slower its rotation. A dark matter halo can The bar extends to its CR. slow down the bar if its mass dominates the central part of the galaxy.

Hohl 1971, ApJ, 168, 343

23 24 Ostriker-Peebles Criterion

Barred Galaxies Barred Galaxies What happens to the other 1/3 of spirals without bars? Stability of m = 2 (bar) perturbation: Ostriker-Peebles criterion

Ostriker-Peebles criterion. Combine two stability factors, Toomre’s Q and the dark halo into one criterion. Critical parameters T t = rot , Φ

where Trot is the kinetic energy of the ordered motion and Φ is the Simulations potential. The virial theorem gives T + T = Φ/2. with Dark rot rand −

Numerical simulations determine that systems with t

Resonance perpendicular to the plan !p = ! " !z /2 LOS parallel to the bar: box-shaped LOS perpendicular to the bar: peanut-shaped

Combes & Sanders 1981, A&A, 96, 164

27 28 Periodic Orbits (II) Periodic Orbits (III)

Barred Galaxies Barred Galaxies 29 30 Curved Dust Lanes Hydrodynamic Simulations

Barred Galaxies Barred Galaxies NGC 5383 Hydrodynamic simultions of the flow of gas in a rotating barred potential (self-gravity not included) Open spirals when there are two resonances (CR & OLR) Tight spirals when inner resonances also present (ILRs, CR, & OLR)

NGC 1097

Credit: Pat Balfour/Adam Block/ NOAO/AURA/NSF

Thin, curved dust lanes mark the leading edge of the bar

Credit: R. Jay GaBany

31 32 A Bar v.s. Tidal Force Gas

Barred Galaxies Barred Galaxies

Spiral waves created by the NGC 1365 barred potential (wide-open) Stream or by the tidal force of a companion (wind up several turns) Lines NGC 5364 Gas tends to follow stellar orbits but its viscosity causes the stream lines to rotate 90° at each resonance Periodic stellar orbits:

x1 family: parallel to the bar, inside IILR or between OILR and CR

x2 family: perpendicular to the bar, between IILR and OILR Credit: David W. Hogg, Michael R. Blanton, & SDSS Credit: FORS Team, 8.2-meter VLT Antu, ESO 33 34 Response of the Gas NGC 1300 as an Example

Barred Galaxies Barred Galaxies

Dust lanes (compression) are created by shock waves, which are created by the abrupt turns of the gas stream lines. Require ILRs hence a slow rotating bar (small !p).

Credit: Hubble Heritage Team, ESA, NASA Athanassoula 1992, MNRAS, 259, 345

35 36 Gas-Cloud Collisions Gas-Cloud Simulations

Barred Galaxies Barred Galaxies Interstellar medium Not continuous interstellar gas Ensemble of molecular clouds Dissipated Energy Composed of dense clouds with a small volume filling factor (3%) immersed in a coronal medium, which is too hot to develop shock waves The density of spiral waves is determined by the energy dissipation through collisions

Problems with continuous fluid models Introducing artificial viscosity Subject to cell size: perfectly inelastic collisions on scales of the order of the cell (grid dependent) Excessive viscosity Lifetime of spiral is short and depends on spatial resolution

Combes & Gerin 1985, A&A, 150, 327 37 38 Torques Exerted Formation of Outer Rings

Barred Galaxies Barred Galaxies by a Bar on the Torques tend to slowly depopulate the CR Gas accumulates at the OLR and forms a ring CR & OLR Gas drift out

ILR & CR fall in Tangential forces on average cancel along circular orbits or elliptical orbits aligned with the major or minor axis of the bar. As soon as the gas forms a spiral, the orbits are elongated, misaligned with the bar and a torque exerts on it. Inside ILR drift out or fall in Schwarz 1984, MNRAS, 209, 93

39 40 Galaxies with Outer Rings

Barred Galaxies Barred Galaxies NGC 2859 NGC 3504

Rings at the NGC 3945 Inner ILR

Form more quickly than the ring at OLR When two ILRs are present, the gas ring forms at the IILR. Credit: D. W. Hogg, M. R. Blanton, & SDSS 41 42 Galaxies with Nuclear Rings Galaxies with Nuclear Rings

Barred Galaxies Barred Galaxies NGC 1097

NGC 4313 Nuclear ring

Credit: Benedict (U. of Texas), NASA Credit: R. Jay GaBany (Cosmotography.com)

Gerin, Combes, & Nakai 43 44 1988, A&A, 203, 44 Nuclear Rings CO Molecular

Barred Galaxies Barred Galaxies Rings in Galactic

Hummel, van der Hulst, & Keel 1987, A&A, 172, 32 Centers

Sakamoto et al. 1999, ApJ, 525, 691 45 46 Double-Barred Double-Barred Galaxies (II)

Barred Galaxies Barred Galaxies Galaxies (I) NGC 1365

Strong bar will bring a large NGC 5728 amount of gas to the center; the rotation curve changes and increase the precession ! " !/2.

Two ILRs appear and the x2 family weakens the bar. A secondary bar decouple from the primary one, rotating much faster with its CR corresponding to the ILR of the primary bar.

Credit: ESO