Interpretation of HFQPOs as hydrodynamic disk modes near compact objects

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Interpretation of HFQPOsas hydrodynamic disk
modesnear compact objects

• M. Hakan Erkut

January 5, 2008 Sabanci University, Karaköy Center
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Outline

• Brief summary of QPO observations
• Characteristic frequencies in accretion disks
• Hydrodynamic effects on the amplification and
  suppression of oscillatory modes in accretion
  disks around NS and BH
• Your questions and comments

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Observations

• PDS of accreting NS and BHs (LMXBs) exhibit QPOs
  with a frequency range of around 0.1-1000 Hz.
• NS systems NBOs ( 5-20 Hz) HBOs ( 15-60 Hz)
• Broad-band noise
  components
• Twin kHz QPOs (
  200-1200 Hz)
• (e.g. AMPs Type-I X-ray Bursters)
• BH candidates LF QPOs ( 0.1-10 Hz)
• HectoHz QPOs (
  100-300 Hz)

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Observational properties of HFQPOs

• All QPO frequencies increase with mass accretion
  rate
• Usually observed as pairs (twin kHz QPOs) in NSs
  and single/pairs in BHs
• Frequency ratios in BHs (7 sources) 3/2 (3
  sources), 5/3 (1 source)
• No specific frequency ratios in NSs
• Peak separation between upper lower kHz QPO
  frequencies in NSs is related to burst (spin)
  frequency of NS
• Peak separation between upper lower kHz QPOs in
  NSs decreases with increasing QPO frequencies

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Burst profile (4U 1728-34)
Strohmayer et al. 1996
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Sco X-1
van der Klis et al. 1997
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4U 1608-52
Méndez et al. 1998
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Correlations between kHz QPO frequencies4U
1728-34
Méndez van der Klis 1999
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Méndez van der Klis 1999
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Psaltis et al. 1998
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Sco X-1
Psaltis et al. 1998
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Low fractional widths, dependence on mass
accretion rate and tight correlations between
QPOs suggest QPOs originate at some preferred
radius/radii in accretion disks around COs.
What do QPOs tell us about their origin?

• Study of hydrodynamic oscillatory modes in
  accretion disks is therefore a necessary first
  step to understand QPO phenomenology

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Characteristic frequencies of accretion disks
Dynamical
Radial epicyclic frequency
Orbital frequency
Vertical oscillation frequency
where
Hydrodynamic
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Global linear mode analysis of fluid equations at
a characteristic radius r
NS
BH
Hydrodynamic free oscillation modes
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Linear mode analysis at a characteristic radius r
For negligible HD corrections, all
eigenfrequencies are real!
Stable Modes !!!
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We must take account of HD corrections to
identify growing/decaying modesand to find the
specific radii in accretion disk at which these
modes are amplified!
In general, all eigenfrequencies are complex
functions!
where
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Characteristic disk frequencies in the
boundary layer (BL) of the
inner disk-NS magnetosphere
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Frequencies (real parts) of hydrodynamic disk
modes in the NS-disk BL
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Growth rates (imaginary parts) of hydrodynamic
disk modes in the NS-disk BL
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Orbital radial epicyclic frequencies for a disk
around a Schwarzschild BH
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Relativistic frequencies(mimic GR using a
pseudo-Newtonian potential)Kerr (Schwarzschild,
a 0) metric
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Frequencies (real parts) of hydrodynamic disk
modes in the inner disk around a
Schwarzschild BH
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Growth rates (imaginary parts) of
hydrodynamic disk modes in the inner
disk around a Schwarzschild BH