Accreting Neutron Stars,Equations of State,

andGravitational Waves

C. B. MarkwardtNASA/GSFC and U. Maryland

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

“Low Mass” X-ray Binaries

Accretion Disk

Companion Star

Neutron Star

from binsim (R. Hynes)

Neutron star primarySecondary companionAccretion torque• spin-up

Inner Most Stable Orbit

Miller Lamb & Psaltis 1998

Long-Term Behaviors

Quasi-regular recurrence

TransientVariable, Turn-off

Turn-on

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

Podsiadlowski Rappaport & Pfahl 2002

Start Grid

Detached

Interacting

Most of the mass is lost from the system

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

RXTE scans of the galactic center (twice per week)

Chandra Galactic Center Image

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)

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

SAX J1808.4-3658 Orbital Doppler Modulation

Accreting X-ray Millisecond Pulsars

Galloway 2007

Spin Distribution

Apparent Cut-off Spin Frequency ~730 Hz

Chakrabarty 2008

RXTE could detect higher frequencies but does not

Thermonuclear Burst Oscillations

X-ray light curve

Power Spectrum – coherent pulsations

Strohmayer & Markwardt 1998

Pulsar and Burster Frequency Distribution

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

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)

KiloHertz Oscillations

FREQUENCY FLUX

Lower Peak

UpperPeak

POWER SPECTRUM

Lower Peak

Upper Peak

Separation

van der Klis 2006

• Various QPOs and peaked noise components for an Atoll source

van Straaten van der Klis & Wijnands 2004

kHz QPOskHz QPOs

1330 Hz

van der Klis 2006

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)

KiloHertz Controversy

Watts et al 2008; Mendez & Belloni 2007

If SPIN = SEPARATION

Known Spins vs. kHz QPO Separation

KiloHertz Controversy

Watts et al 2008; Mendez & Belloni 2007

If SPIN = SEPARATION

Known Spins vs. kHz QPO Separation

If Half SPIN = SEPARATION

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

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)

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

KiloHertz Constraints

Miller Lamb & Psaltis 1998

Example upper

frequency

Example upper

frequency

KiloHertz Constraints

Miller Lamb & Psaltis 1998

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

Cackett et al 2007

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

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

Pulse Phase Noise

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

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