Accreting Neutron Stars, Equations of State, and Gravitational Waves

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Accreting Neutron Stars,Equations of
State,andGravitational Waves

• C. B. MarkwardtNASA/GSFC and U. Maryland

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Taxonomy of X-ray Binaries
Accreting Binary
Low Mass X-ray Binaries (Mc lt 1Mo)

• High Mass X-ray Binaries (Mc gt 1Mo)
• slow pulsars
• often wind-fed
• eg, Vela X-1

• Atoll sources
• Low mass accr rate (lt 0.1 MEdd)
• eg, SAX J1808.4-3658

• Z sources
• High mass accr rate (gt 0.1 MEdd) higher B
  field?
• eg, Sco X-1

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Low Mass X-ray Binaries

• Neutron star primary
• Secondary companion
• Accretion torque
• spin-up

from binsim (R. Hynes)
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Inner Most Stable Orbit
Miller Lamb Psaltis 1998
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Long-Term Behaviors
Turn-on
Quasi-regular recurrence
Transient
Variable, Turn-off
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Synthesis of X-ray Binaries

• Formation of binary star system
• Complex evolutionary scenarios
• Stellar evolution
• Mass transfer
• Stable Roche lobe overflow
• Runaway, common envelope
• Binary interaction
• Magnetic braking
• Orbital gravitational radiation
• Typical low mass X-ray binary is old
• Progenitors of millisecond radio pulsars

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Start Grid
Detached
Interacting
Most of the mass is lost from the system
Podsiadlowski Rappaport Pfahl 2002
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Specialized Detection Methods

• Rossi X-ray Timing Explorer
• High collecting area, high time resolution
• Poor spatial resolution (1? full-width half max)
• All Sky Monitor for bright sources

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• RXTE scans of the galactic center (twice per week)

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Chandra Galactic Center Image
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Observational Properties

• Neutron star parameters
• Spin frequency ( derivative, phase noise)
• X-ray Pulse shape
• Orbit parameters
• Period, inclination, a sin i, epoch of node
• System parameters
• Mass transfer rate
• Nature of companion (companion spectroscopy)

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Observational Status

• 10 accreting millisecond X-ray pulsars
• Coherent pulsations 180-600 Hz
• High quality orbit determinations (periods 1-5
  hr)
• Transient behavior with low duty cycle
• Durations 10-200 days, recurrences 2-5 years
• 16 burst oscillation sources
• Brief oscillations during thermonuclear
  detonations on neutron star surface
• Inferred to be close to NS spin rate, perhaps
  burning hot-spot on NS surface
• Confirmed by XTE J1814-338, SAX J1808.4-3658
• Highly coherent oscillations during superburst of
  4U 1636-536
• 10 kHz pair sources
• Measured separation between two variability peaks
  in the X-ray power spectrum
• Low theoretical confidence of emission mechanism
• Few orbital constraints
• Many 10s of systems with no spin information

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SAX J1808.4-3658 Orbital Doppler Modulation
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Accreting X-ray Millisecond Pulsars
Galloway 2007
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Spin Distribution
Apparent Cut-off Spin Frequency 730 Hz
RXTE could detect higher frequencies but does not
Chakrabarty 2008
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Thermonuclear Burst Oscillations
Power Spectrum coherent pulsations
X-ray light curve
Strohmayer Markwardt 1998
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Pulsar and Burster Frequency Distribution
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Speed Limit?

• Bildsten 1998 had suggested that if a spinning
  neutron star could form and sustain a large
  enough quadrupole moment, spin frequency could be
  limited by gravitational radiation
• Assuming the NS is at spin equilibrium due to GR
  emission, the strain at earth would be
• To explain data, require ellipticity 10-7

X-ray Flux
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Overview of Mechanisms

• Mountains
• Thermal induced crustal cracking (Bildsten 1998)
• Magnetically confined accretion mounds (Melatos
  et al)
• Rossby-waves in core (Andersson et al 1999)
• Non gravitational-wave
• Magnetic dipole radiation (SAX J1808, B 108 G)
• Magnetic coupling to accretion disk (Ghosh Lamb
  1978)

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KiloHertz Oscillations
POWER SPECTRUM
UpperPeak
Upper Peak
Lower Peak
Lower Peak
Separation
van der Klis 2006
FREQUENCY
FLUX
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kHz QPOs

• Various QPOs and peaked noise components for an
  Atoll source

van Straaten van der Klis Wijnands 2004
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1330 Hz
van der Klis 2006
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KiloHertz QPO Interpretations

• Frequency separation is nearly constant, and
  equal to the spin frequency (or half the spin
  frequency)
• Upper frequency represents a characteristic
  frequency near the innermost stable orbits
• Various models such as sonic point to explain
  QPOs as beat frequencies or vertical vs. radial
  epicyclic frequencies (Miller Lamb Psaltis
  1998 Titarchuk 2001)

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KiloHertz Controversy
Known Spins vs. kHz QPO Separation
If SPIN SEPARATION
Watts et al 2008 Mendez Belloni 2007
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KiloHertz Controversy
Known Spins vs. kHz QPO Separation
If SPIN SEPARATION
If Half SPIN SEPARATION
Watts et al 2008 Mendez Belloni 2007
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Equation of State of Accreting Neutron Stars

• Several attempts to measure the equation of state
• Redshift at neutron star surface
• Pulse shape fitting
• Relativistic broadening of Fe lines
• KiloHertz QPO interpretations

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Gravitational Redshift

• Cottam et al 2002 claimed detection of redshifted
  Fe absorption lines from EXO 0748-676 neutron
  star surface (z0.35), providing a constraint on
  compactness GM/Rc2 0.22
• Independent measurement of neutron star spin, 45
  Hz (Villareal Strohmayer 2004), and Doppler
  broadening, in principle provide independent
  constraints on M and R
• The redshifted line feature was never detected in
  any subsequent observations (both in follow-up
  observations of EXO 0748-676 and GS 1826-24)

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X-ray Pulsar Pulse Shape Fitting

• For msec X-ray pulsars, fundamental and harmonic
  content provides some constraint on the
  compactness of the star M/R (Poutanen et al 2003)
• Also requires modeling of emission region

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KiloHertz Constraints
Example upper frequency
Miller Lamb Psaltis 1998
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KiloHertz Constraints
Miller Lamb Psaltis 1998
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Relativistically Broadened Lines

• Detection of broadenedlines from accretiondisk
  around LMXBs,including msec X-raypulsar SAX
  J1808.4-3658
• Must reliably distinguishbroadened line emission
  from continuum, and model accurately

Cackett et al 2007 Cackett et al 2009
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Cackett et al 2007
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Prospects for Detecting Gravitational Waves

• Watts et al 2008 performed an extensive
  feasibility study of detecting accreting neutron
  stars
• Considered all classes (msec X-ray pulsars, X-ray
  bursters, kHz QPO sources)
• Assumed spin equilibrium due to gravitational
  wave emission (mountain and r-mode scenarios)
• Ignored complicating effects of disk interaction
  (Ghosh Lamb 1978), spin derivative, pulse noise
• Estimated sensitivies based on number of trials
  and uncertainties in spin/orbit parameters

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Complicating Effects

• Spin change
• considered in Watts study, but
• SAX J1808.4-3658 spinDOWN occurs mostly during
  quiescence can be explained by magnetic dipole
  radiation
• Difficult to know spin-up/down for other sources
  from only one or two outbursts
• Orbital period derivative is positive, not easily
  explained (di Salvo et al 2008 Hartman et al
  2009)

Spin Evolution
Orbit Evolution
Hartman et al 2009
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Pulse Phase Noise

• Significant phase noise and trends are
  controversial
• Spin changes?
• Pulse profile changes? (i.e. emission region)

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Conclusion

• Detecting gravitational waves from accreting
  neutron stars will be a challenge
• Tracking spin phase over long durations will be
  difficult because of the secular trends and
  stochastic variabilities these sources exhibit
• Recommend semi-coherent stacking methods
  instead of fully coherent folds
• Methods will unfortunately need to attempt to
  model gradual spin and orbital changes