1. Accreting Neutron Stars, Equations of State, and Gravitational Waves C. B. Markwardt NASA/GSFC and U. Maryland

2. Taxonomy of X-ray Binaries Low Mass X-ray Binaries (M c < 1M o ) Accreting Binary High Mass X-ray Binaries (M c > 1M o ) slow pulsars often wind-fed eg, Vela X-1 “Atoll” sources Low mass accr rate (< 0.1 M Edd ) eg, SAX J1808.4-3658 “Z” sources High mass accr rate (> 0.1 M Edd ); higher B field? eg, Sco X-1

3. “Low Mass” X-ray Binaries Accretion Disk Companion Star Neutron Star from binsim (R. Hynes) Neutron star primary Secondary companion Accretion torque spin-up

4. Inner Most Stable Orbit Miller Lamb & Psaltis 1998

5. Long-Term Behaviors Quasi-regular recurrence TransientVariable, Turn-off Turn-on

6. 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

7. Podsiadlowski Rappaport & Pfahl 2002 Start Grid Detached Interacting Most of the mass is lost from the system

8. 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

9.  RXTE scans of the galactic center (twice per week)

10. Chandra Galactic Center Image

12. 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)

13. 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

14. SAX J1808.4-3658 Orbital Doppler Modulation

15. Accreting X-ray Millisecond Pulsars Galloway 2007

16. Spin Distribution Apparent Cut-off Spin Frequency ~730 Hz Chakrabarty 2008 RXTE could detect higher frequencies but does not

17. Thermonuclear Burst Oscillations X-ray light curve Power Spectrum – coherent pulsations Strohmayer & Markwardt 1998

18. Pulsar and Burster Frequency Distribution

19. 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

20. 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 ~ 10 8 G) – Magnetic coupling to accretion disk (Ghosh & Lamb 1978)

21. KiloHertz Oscillations FREQUENCYFLUX Lower Peak Upper Peak POWER SPECTRUM Lower Peak Upper Peak Separation van der Klis 2006

22. Various QPOs and peaked noise components for an Atoll source van Straaten van der Klis & Wijnands 2004 kHz QPOs

23. 1330 Hz van der Klis 2006

24. 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)

25. KiloHertz Controversy Watts et al 2008; Mendez & Belloni 2007 If SPIN = SEPARATION Known Spins vs. kHz QPO Separation

26. KiloHertz Controversy Watts et al 2008; Mendez & Belloni 2007 If SPIN = SEPARATION Known Spins vs. kHz QPO Separation If Half SPIN = SEPARATION

27. 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

28. 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/Rc 2 ~ 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)

29. 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

30. KiloHertz Constraints Miller Lamb & Psaltis 1998 Example upper frequency

31. KiloHertz Constraints Miller Lamb & Psaltis 1998

32. Relativistically Broadened Lines Detection of broadened lines from accretion disk around LMXBs, including msec X-ray pulsar SAX J1808.4-3658 Must reliably distinguish broadened line emission from continuum, and model accurately Cackett et al 2007 Cackett et al 2009

33. Cackett et al 2007

34. 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

36. 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

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

38. 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