accreting neutron stars, equations of state, and gravitational waves c. b. markwardt nasa/gsfc and...
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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
Low Mass X-ray Binaries (Mc < 1Mo)
Accreting Binary
High Mass X-ray Binaries (Mc > 1Mo)• slow pulsars• often wind-fed• eg, Vela X-1
“Atoll” sources• Low mass accr rate (< 0.1 MEdd)• eg, SAX J1808.4-3658
“Z” sources• High mass accr rate (> 0.1 MEdd); higher B field?• eg, Sco X-1
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“Low Mass” X-ray Binaries
Accretion Disk
Companion Star
Neutron Star
from binsim (R. Hynes)
Neutron star primarySecondary companionAccretion torque• spin-up
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Inner Most Stable Orbit
Miller Lamb & Psaltis 1998
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Long-Term Behaviors
Quasi-regular recurrence
TransientVariable, Turn-off
Turn-on
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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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Podsiadlowski Rappaport & Pfahl 2002
Start Grid
Detached
Interacting
Most of the mass is lost from the system
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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
Chakrabarty 2008
RXTE could detect higher frequencies but does not
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Thermonuclear Burst Oscillations
X-ray light curve
Power Spectrum – coherent pulsations
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
FREQUENCY FLUX
Lower Peak
UpperPeak
POWER SPECTRUM
Lower Peak
Upper Peak
Separation
van der Klis 2006
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• Various QPOs and peaked noise components for an Atoll source
van Straaten van der Klis & Wijnands 2004
kHz QPOskHz QPOs
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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
Watts et al 2008; Mendez & Belloni 2007
If SPIN = SEPARATION
Known Spins vs. kHz QPO Separation
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KiloHertz Controversy
Watts et al 2008; Mendez & Belloni 2007
If SPIN = SEPARATION
Known Spins vs. kHz QPO Separation
If Half SPIN = SEPARATION
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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 (z=0.35), 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
Miller Lamb & Psaltis 1998
Example upper
frequency
Example upper
frequency
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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 2007Cackett 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