DDA 2015 – Bringing Black Holes Together: Plunging through the Final Parsec

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Kelly Holley-Bockelmann (Vanderbilt)

Abstract

[None]

Notes

  • How to bringBHs together: three phases
    • Galaxy mergers sinkBHs through dynamical friction
      • $\sim 10^5$ pc
    • Sink closer via 3-body scattering
      • Quinlan 1997
      • dynamical friction no longer operating
      • $\sim 10$ pc, $\sim 10^{10}$ yr(!?)
    • Finally, GW complete the merger
      • $\sim 10^{-5}$ pc
  • Problem: once loss coneis depleted by 3-body scattering, it can only be refilled by 2-body relaxation
    • Merger stalls at $\sim 1$ pc
      • hence the “final parsec problem”
    • Begelman, Blandford, & Rees 1980, Makino 1997, Merritt & Milos 2005
  • Solution: galaxies are not idealized gas-free, stable, equilibrium systems!
    • Mayer et al. 2007: galaxies have gas; gas drives theBHs closer
      • drag(?)
      • spiral wave torques
      • problem: AGN feedback
    • Ostriker,Binney, & Silk 1989: galaxies aretriaxial
      • triaxiality introduces new mechanisms for phase space transport
        • chaos
        • Berczik et al. 2005
      • gets you to grav radiation regime
    • Khan,KHB,Berczik, and Just 2013: test limits of 3-body scattering
      • N-body sims
      • gas-poor, non-rotating, axisymmetric potential
      • still takes too long (2.5 Gyr)
      • found special orbits to fill loss cone
        • because near BH the potential istriaxial
          • even closer, is spherical
        • $\rightarrow$ changes in shape are important
      • add rotation $\rightarrow$ merger goes faster (yay)
        • axisymmetric, counter-rotating: ~100 Myr
          • but eccentricities very high

DDA 2015 – p-ellipse Orbit Approximations, Lindblad Zones, and Resonant Waves in Galaxy Disks

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Curtis Struck (Iowa State)

Abstract

p-ellipses are simple, yet very accurate formulae for orbits in power-law potentials, like those approximating galaxy disks. These precessing elliptical orbits reveal important systematics of orbits in such potentials, including simple expressions for the dependence of apsidal precession on eccentricity, and the fact that very few terms (or parameters) are needed for the approximation of even nearly radial orbits. The orbit approximations are also useful tools for addressing problems in galaxy dynamics. In particular, they indicate the existence of a range of eccentric resonances associated with the usual, near-circular Lindblad resonances. Collectively these change an isolated Lindblad resonance to a Lindblad Zone of eccentric resonances. A range of these resonances could be excited at a common paRern speed, aiding the formation of a variety of bars and spirals, out of eccentric orbits. Such waves would be persistent, and not wind up or disperse, since differences in their precession frequencies offset differences in the circular velocities at the radii of their parent orbits. The p-ellipse approximation further reveals how a non-axisymmetric component of the gravitational potential (e.g., due to bar self-gravity) significantly modifies precession frequencies, and similarly modifies the Lindblad Zones.

Notes

  • Precessing ellipses
    $\dfrac{1}{r} = \dfrac{1}{p}\left[1+e \cos (m \phi)\right]^{\frac{1}{2}+\delta}$
    yield good fits for orbits in different potentials
  • Apsidal precession:
    $\Delta \phi = \dfrac{\pi}{\sqrt{2(1-\delta)}}$
    $\rightarrow$ kinematic waves, bars
  • Nearly radial orbits: p-ellipse fits not so good
  • But can tweak to get good fits:
    • Fit to the extremal radii, not the position
    • Note that apsidal precession is not constant but depends on eccentricity
    • Add harmonic terms:
      $\dfrac{1}{r} = \dfrac{1}{p}\left[1+e_1 \cos (m \phi)+e_2 \cos (2 m \phi)\right]^{\frac{1}{2}+\delta}$
  • Example of (possibly) kinematic counter-rotating waves: NGC 4622
  • Summary
    • Accurate, simple approximations for orbits in a range of potentials
    • Can be extended to radial orbits
    • Turns Lindblad resonances into Lindblad zones
    • Allows formation of persistent kinematic waves of various types
      • but usually requires fine tuning

DDA 2015 – The Relative Influence of Dynamical Nature and Nurture on the Formation of Disk Galaxies

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Jonathan Bird (Vanderbilt) (invited)

Abstract

[None]

Notes

  • Are disk galaxies formed by nature or nurture?
  • e.g. NGC 891
  • Thick disk and thin disk (Gilmore & Reid 1983)
    • Extragalactic thick disks are ubiquitous (Dalcanton & Bernstein 2002, Yoachim & Dalcanton 2006)
  • Nature:
    • Stellar kinematics dominated by those of gas from which stars formed
    • Subsequent dynamics are second-order
    • Planetary disk: core accretion; static
    • $\alpha$ abundance is a tracer for stellar age
      • plot: [$\alpha$/Fe] vs [Fe/H]
      • Thick disk is old, $\alpha$-rich, kinematically hot
      • Thin disk is young, (relatively to Fe) $\alpha$-poor, dynamically cold
    • Smooth correlation between chemistry and kinematics
    • APOGEE survey: velocity dispersion increases with stellar age
      • power law
      • $\rightarrow$ disk grows over time
  • Nurture:
    • Stellar kinematics dominated by dynamical interactions after birth
    • Most stars born in dynamical cold gas (level playing field)
    • Resonances play huge role; pebble accretion
    • Scattering processes heat stellar velocity distributions
    • Radial migration
      • Sellwood & Binney 2002: can redistribute stars without globally heating the disk
      • Can outwardly migrating stars create the thick disk?
      • No: vertical action is conserved. (Tolfree et al. 2014)

DDA 2015 – Instabilies in Near-Keplerian Systems

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Anne-Marie Madigan (UC Berkeley) (invited)

Abstract

Closed orbits drive secular gravitational instabilities, and Kepler potentials are one of only two potentials in which bound orbits are closed. Though the Kepler potential is common in astrophysics — relevant for stars orbiting massive black holes in the centers of galaxies, for planets orbiting stars, and for moons orbiting planets — few instabilities have been explored beyond the linear regime in this potential. I will present two new instabilities which grow exponentially from small initial perturbations and act to reorient eccentric orbits in near-Keplerian disks. The first results from forces in the plane of the disk and acts to spread orbits in eccentricity. The second instability results from forces out of the disk plane and drives orbits to high inclination. I will explain the dynamical mechanism behind each and make observational predictions for both planetary systems and galactic nuclei.

Notes

  • Why Kepler potentials?
    • Only two potentials yield closed orbits: $\psi \sim -\frac{1}{r}$, $\psi \sim r^2$
    • More general, richer dynamics (than quadratic potentials)
  • Eccentric disk instability
    • Madigan 2009
    • Galactic center vs. Andromeda nucleus
      • single peak vs. double peak (in luminosity)
      • Presence/absence of nuclear star cluster changes direction of apsidal precession.
      • Andromeda: apsidally aligned orbits $\rightarrow$ double luminosity peak
    • Prograde precession case
      • torque from disk grav. reducesang. momentum, increasing eccentricity.
        • produces oscillations
        • but stable disks
      • Andromeda
    • Retrograde precession:
  • Inclination instability
    • Madigan 2015
    • Thick disk of stars in Galactic center
    • Dwarf planets (inner Oort Cloud)are clustered in $\omega$. How?
      • $\cos \omega = \dfrac{\sin i_a}{\sin i_b}$ (inclinations wrt major and minor axes)
      • Dwarf planets are clustered in $\omega$ because high eccentricity orbits in a disk are unstable.
    • In Galactic center, ~80% of young stars are not in disk plane (Yelda 2014). How did they get there?
    • Set by initial inclinations.
    • Two-body diffusion stage, then ~sudden instability.
    • Instability grows exponentially.