1. Probing the Neutron Star Equation of State and Synergy with Advanced LIGO and Virgo Cole Miller University of Maryland

2. 2 Outline What we know about dense matter now Methods of constraining M and R from X-ray observations, and benefits of new observatories The promise of gravitational waves Main point: larger area with good timing and energy coverage is important to test models and reduce systematics, as well as to reduce statistical uncertainties.

3. 3 Dense Matter Matter in NS core is several times nucl. density Only nucleons? Quark matter? Strange matter? Condensates? NS mass vs. radius, maximum mass would provide clues Theoretical curves: NS mass vs. radius

4. 4 A 1.97 M sun Neutron Star! PSR J1614-2230 NS-WD system, almost exactly edge-on Allows precise measurement of both masses No classical contributions! M=1.97+-0.04 M sun Hard EOS, minimal exotica? But modelers can adjust More to come, due to improved timing for pulsar array GW detection Demorest et al. 2010

5. 5 Radius: The Final Frontier Unlike mass, which has effects at a distance, radius is much tougher to measure All proposed methods suffer from large and often unknown systematics, and lack of enough data to resolve them Key: larger area esp. with good timing IXO, LOFT, GRAVITAS, AXTAR, NICER We now discuss example methods

6. 6 X-ray Burst Analysis If we assume full surface radiates uniformly in tail, and that we know Eddington lum, composition, and spectrum, get mass and radius (van Paradijs 1979) Analysis assuming no systematics gets tight constraints. But evidence is mounting for non-uniform emission and problems with spectrum. For example, standard assumptions give no solution for M and R unless observables are pushed to improbable extremes (Steiner et al. 2010) Guver et al. 2010; 4U 1820-30

7. 7 Note on bursts: we are currently analyzing RXTE PCA data from the 4U 1820-30 superburst using detailed spectral models. We have prospects of constraining both the surface gravity and redshift, which would in turn constrain M and R. Stay tuned! Work with Fred Lamb and Ka Ho Lo (Illinois), Stratos Boutloukos and Valery Suleimanov (Tuebingen), and Juri Poutanen (Oulu)

8. Ray Tracing and Light Curves Rapidly rotating star 300-600 Hz v surf ~0.1c SR+GR effects Light curve informative about M, R Miller & Lamb 1998 Bogdanov+ 2007,8 Many others... Key: need multiple harmonics, more area (e.g., NICER, LOFT) Weinberg, Miller, and Lamb 2001

9. 9 Cooling NS Observations Transient accretion, cooling Predictions: Minimum level of emission Spectrum should be thermal Not variable; slow, steady decay Oops! All the predictions fail L below minimum Large power law component Significant variability, even in thermal component Some possible explanations (e.g., residual accretion), but troubling We also need more counts to ensure that our continuum models are correct, hence that our temperatures are right Jonker 2007

10. 10 Information from Gravitational Waves Inspiral of NS into NS, or into BH; aLIGO/aVirgo tens/year To lowest order, inspiral described by (Peters 1964): Here M is the total mass and  is the symmetric mass ratio m 1 m 2 /M 2.  reaches max of 0.25 for m 1 =m 2. Chirp mass M ch 5/3 =  M 5/3 will be measured to high precision. But a (much tougher) measurement of  is needed to get both masses independently. Maybe for strongest sources. What about radius?

11. Radius Measurements from GW? BH-BH: point masses With NS, have tidal effects Can look for disruption, or for deviations from inspiral BH-NS not as promising unless BH are very low mass (NS swallowed nearly whole; Miller 2005) New theory needed of tidal deformation near merger; with this, strongest events would significantly constrain radius (Hinderer et al. 2010) BH-BH: Baker NS-NS: Faber

12. 12 Conclusions NS masses ~2 M s are established Radii still very much up in the air: all current methods suffer from systematics Larger area instruments are key Improve statistics; more importantly, will allow systematics to be tested In ~5 years, GW obs very important

13. 13 Original fig: Dany Page

14. 14 Information from Gravitational Waves Next gen of GW detectors could see many NS-NS, NS-BH Can get info on masses and possibly radii

15. 15 The Symmetric Mass Ratio To break degeneracy, must learn  as well as the chirp mass But over reasonable NS- NS mass ratios,  varies little Also, only higher-order effects in GW allow determination of  Precisions will be lower

16. BH-NS: The Problem of Spin Mass ratio more extreme, so  sensitivity not as great But BH can spin rapidly, unlike NS in high-mass binary Introduces precession: complicates waveforms Etienne et al. 2009

17. Tidal Measurement in Practice For AdLIGO, even strong sources will not give phase signals to 450 Hz that allow EOS to be distinguished But much theoretical development remains At higher freq, tidal effects are much stronger Work is underway! Figs from Hinderer et al. 2010

18. 18 Caveats and Status of Ray Tracing One might think spot shape matters, but for small spots shape is irrelevant Broad view of surface, plus light deflection Beaming pattern does matter some; choose electron scattering or isotropic emission Current constraints are not restrictive, but future large-area instruments might get radius to 5% or better But always beware of systematic uncertainties in detector response and model!

19. 19 Emission from Cooling NS Old, transiently accreting NS e capture releases energy deep in crust If know average accretion rate, emission provides probe of cooling (neutrinos especially) Predictions of simple model: Minimum level of emission Spectrum should be blackbody No variability: steady, slow decay

20. 20 Radii from qLMXB in Globular? Just statistical errors. Assumes perfect distance knowledge. Fixes mass of star at 1.4 M s Fixes spectral model (pure hydrogen, no mag field) For best source (#1), 49% of emission in power law; what causes this? Continuum spectra not great for constraints! Data assembled from Guillot, Rutledge et al. 2008

21. 21 Alternate Gravity Theories? Keep in mind: strong gravity not tested well Therefore, really testing joint hypothesis of EOS and gravity Just cautionary, though, and LIGO grav waves should test strong GR DeDeo & Psaltis 2003

22. 22 Relevance: the High kT Problem Balance of grav, rad accel gives maximum surface flux (indep of distance, luminosity of source). For a NS mass M, maximizing BB temp at infinity over redshift gives (see also Marshall 1982) for pure He or heavy element (1.71 keV for pure H). However, best fit BB temps often kT~3.0 keV (known for 30 years). Assumed that color factor will reduce this to kT eff <2.0 keV. But such large spectral distortions should leave their imprint. What do data say?

23. 23 A Long Shot: Quasi-Periodic Oscillations X-ray intensity from NS LMXBs varies quasi- periodically Best model: upper peak close to orbital frequency at some special radius Some evidence for ISCO M~2M s ? Sco X-1 (van der Klis et al. 1996)

24. 24 A Long Shot: Quasi-Periodic Oscillations X-ray intensity from NS LMXBs varies quasi- periodically Best model: upper peak close to orbital frequency at some special radius Some evidence for ISCO M~2M s ? M-R constraints: Miller et al. 1998

25. 25 The Innermost Stable Circular Orbit GR “pit in the potential”: gravity is stronger than Newtonian Minimum in L Unstable for r<6M Matter falls in rapidly Lower limit to disk radius If QPO at ISCO, know mass! How to identify ISCO? Specific angular momentum vs. radius, for Schwarzschild

26. 26 Predicted Behavior at ISCO Barret, Olive, Miller 2005. Expect, and see, sharp drop in quality factor at same freq indep of count rate

27. 27 Complementary Constraints In principle, measurement of speed would add greatly to information Modulo minor frame-dragging effects: f~(GM/r 3 ) 1/2 v~(GM/r) 1/2 Would combine to give independent constraints on mass, orbital (not stellar) radius With frame-dragging, constrain a/M How can speed be measured?

28. 28 Broad Iron Lines Iron fluorescence lines are seen from many BH Profile affected by Doppler, grav. redshifts, and inclination Recently seen from several NS sources Constrains spin and speed Do not yet have single source with simultaneous QPOs, good line data Cackett et al. 2007

29. 29 Radius Measurements in Practice Challenge 1: action at high freq (but accessible) Challenge 2: need to know mass to get radius But might get  R~1 km for strongest sources Read et al. 2009, d=100 Mpc, 1.35-1.35 M s AdLIGO Broadband ET