The Physical Origin of Negative Superhumps

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Introduction

• AM CVn stars show both positive and negative
  superhumps
• Common superhumps shown by Whitehurst and several
  others to be the result of tidal driving of the
  disk at the inner Lindblad resonance
• Patterson et al. (1993) suggested AM CVn
  photometric variations are superhumps in helium
  accretion disks
• Simpson Wood (1998) modeled these disks using
  SPH and found superhumps consistent with the
  observations
• Plots of the energy generation versus time showed
  strong likeness to observed light curves

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Smoothed Particle Hydrodynamics

• SPH is a Lagrangian numerical technique (Monoghan
  1992)
• Kernel interpolation to obtain fluid properties
  and non-gravitational body forces
• Particle size ? smoothing length h
• Time step using the leapfrog method
• Artificial viscosity
• Effectively "point markers" in the fluid

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SPH Lightcurves
Bolometric light curve resulting primarily
from viscous dissipation
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SPH Lightcurves
Note pulse shape is more sawtoothed when pulses
begin and take on a smaller amplitude with more
rounded pulses after a couple dozen cycles,
similar to observed superhumps
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Light curve from q0.25 simulation (Wood,
Montgomery, Simpson 2000) The SH start doesnt
happen until orbit 110 (versus 40 for q0.07).
Once resonance starts, strong SH driven to
non-linearity. System eventually settles down to
quasi-stationary pulseshape.
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q 0.075
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Superhump Oscillation

• The physical origin of the positive superhumps is
  a driven oscillation of the disk (32 resonance)
• It is insufficient to describe positive SH as the
  result of an elliptical precessing disk as
  often seen in the literature it is more complex
  and interesting!
• Bright spot has little effect on the light curve
  the bright spot is not the SH light source

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The SPH Model

• 50,000 particles
• 5,000 particles/orbit for 10 orbits
• Replace accreted/ejected particles at L1
• SH begin near orbit 40
• Light curve calculated from viscous dissipation
  (primarily)
• Visualized using IDL and Adobe Premier

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• Positive Superhumps Movie
• Density Light Curve

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• Positive Superhumps Movie
• Particle Luminosity
• Note in the animation the coming and going of the
  white particles in the spiral arms in the disk
  this is the origin of the observed superhumps
• The arms advance 180 degrees in the co-rotating
  frame once a superhump cycle
• Thus, the two spiral arms alternate in their
  interaction with the secondary
• As viewed in a frame orbiting at 1.5 times the
  superhump frequency (2/3 orbital period), the
  spiral pattern should be roughly stationary
  Doppler tomography may be able to reveal this
  structure, and datasets exist!

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• Apsidal Superhumps in the
• Frame of the Spiral Arms

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Negative (Nodal) Superhumps

• First observed in the mid 1980s as a 5.2-h
  photometric period in TV Col, which has Porb
  5.5 h
• More rare than positive SH, only 17 systems
  known
• Only AM CVn itself has been shown to display
  negative SH among the helium cataclysmics
• Bonnet-Bidaud, Motch, Mouchet (1985) first to
  suggest the 5.2-hr period in TV Col could be the
  signature of an accretion disk which is tilted
  out of the orbital plane and which as a result
  precesses slowly in the retrograde direction.

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Negative SH

• Barrett et al. (1988) also suggested that
  negative SH were involved a freely precessing
  tilted disk, with a magnetic field at L1
  directing the accretion flow out of the orbital
  plane
• They also suggested (!) the negative superhump
  light source was the bright spot migrating across
  the face of the tilted accretion disk
• Our models confirm this suggestion, as we discuss
  below

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The SPH Models

• Assume M1 1.0 Msun, M2 0.4 Msun, which gives
  Porb 4.3 hr
• 50,000 particles
• 4,000/orbit for 12.5 orbits
• Relax simulation to equilibrium solution until
  orbit 100, replacing accreted/ejected particles
  at L1
• Tilt disk by 5 degrees and continue simulation
• Add new burst of particles of 4,000/orbit for 5
  orbits to help visualize the bright spot migration

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Simulation Light Curve
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Neg SH Light Source

• Because we effectively integrate over 4pi sr, our
  light curves peak twice per orbit (? 2.1 orb-1)
• The ray-traced visualizations show that a given
  observer would only see one face of the tilted
  optically-thick disk (? 1.05 orb-1)
• Because the disk has a finite opening angle, as
  the disk precesses the apparent brightness of the
  bright spot crossing will change, leading to the
  beat period of order a few days, for systems
  with i gt 45o or so

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Negative Superhumps The Movie
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Negative Superhumps The Movie Sideways
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Tilting the Disk

• The major question is how to tilt the disk
• Barrett et al. (1988) suggested a magnetic field
  at L1 could direct the flow out of the page (but
  )
• Murray et al. (2002) found that turning on a
  magnetic field on the secondary star would
  warp/tilt the disk (but again )
• Our experiments
• Murrays explanation is probably correct, but
  probably need magnetically-active secondary -gt
  magnetic reconnections can change the field on
  short timescales applying impulses to the disk
  (Hellier 1993 TV Col flare?)

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Conclusions

• The physical origin of both positive and negative
  superhumps is now relatively well understood
• Positive
• Driven oscillation of a disk (not precessing
  elliptical disk)
• Found in models for mass ratios 0.03 lt q lt 0.34
• Models at q 0.075 develop SH fastest very
  very slow at extreme boundaries of the range
• Negative migration of bright spot across the
  face of a tilted precessing disk
• Works for any mass ratio
• Tilt must be more than 3o in the simulations

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Conclusions II

• Future work
• FITDisk Windows GUI SPH toy code (V1.0
  released Fall 2005)
• Viscosity physics (magnetorotational instability)
  
• Radiative transfer
• Inclination dependent light curves
• Velocity map images of real superhumps
• Use models to generate velocity map images for
  comparison with observations
• What really tilts the disks, and how to keep them
  out of the plane?

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Discussion?