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Outline of talk

Constraining Neutron Star Radii and Equations of State Josh Grindlay Harvard (collaboration with Slavko Bogdanov McGill Univ.). Outline of talk. Radii from X-ray bursts (BB fits) Radii from quiescent LMXBs (BB fits) Radii of isolated NSs (e.g. RXJ1856-3754) (J. Truemper’s talk…)

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Outline of talk

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  1. Constraining Neutron Star Radiiand Equations of StateJosh GrindlayHarvard(collaboration with Slavko Bogdanov McGill Univ.)

  2. Outline of talk • Radii from X-ray bursts (BB fits) • Radii from quiescent LMXBs (BB fits) • Radii of isolated NSs (e.g. RXJ1856-3754) (J. Truemper’s talk…) • Radii from MSPs (M/R from light bending)

  3. NS Radii from X-ray bursts • Type I x-ray bursts are thermonuclear flashes on NSs in low mass X-ray binaries (LMXBs) • Some are Eddington limited (flat-topped Lx) with BB radii determined from Lx ~ R2 T4 and measured T at “touchdown” when emission from (entire) NS surface • Best done with LMXB in globular cluster, at well measured distance

  4. Radius Expansion X-ray burst from M15 • M15 burst seen from X2127+119 by RXTE from M15 (d = 10 ±0.5 kpc) by Smale (2001): • Derived NS parameters: R* = 8.6 ±1km (but uncertain by Comptonizing atmosphere model) 1 + z = 1.28 ±0.06 and mass of NS = 2.38 ±0.18 Msun

  5. vs. Spectral line shifts in X-ray burst • Cottam et al (2002, Nature) observed and stacked 28 bursts from EXO 0748-676 • Candidate Fe XXVI lines seen at redshift z = 0.35

  6. Atmospheric radii of quiescent LMXBs • Heinke et al (2006, ApJ) derive constraints on luminous quiescent LMXB X7 in 47Tuc, using NS-atmosphere model of Rybicki et al • Derived RNS = 14.5 ±1.7 km for M = 1.4Msun 1 + z = 1.26 ±0.12 or if R = 10 km M = 2.20 ±0.1Msun

  7. Y R Rotation-powered (“recycled”) millisecond pulsars MSPs are “ideal”: Constant, noise free Binary companions (allow mass meas.) • ~50 MSPs detected in X-rays to date (mostly in globular clusters) • Very faint X-ray sources - LX 1033 ergs s–1 (0.1-10 keV) - typical: LX 1030–31 ergs s–1 • Many exhibit (pulsed) soft, thermal X-ray emission from magnetic polar caps 19 MSPs in 47 Tuc Chandra ACIS-S 0.3-6 keV Bogdanov et al. (2006)

  8.  Thermal X-ray emission due to polar cap heating by a return current of relativistic particles from pulsar magnetosphere e+ X-rays e+ X-rays  The surface radiation can serve as a valuable probe of neutron star properties (compactness, magnetic field geometry, surface composition,…)

  9. Modeling thermal X-ray emission from MSPs Viironen & Poutanen (2004) • Ingredients: -rotating neutron star - two X-rayemitting hot spots - General & special relativity * Schwarzschild metric (good for  300 Hz) * Doppler boosting/aberration * propagation time delays - optically-thick hydrogen atmosphere      = pulsar obliquity  =  b/w line of sight & pulsar spin axis (t) = rotational phase  = photon w.r.t surface normal  = photon  at infinity b = photon impact parameter at infinity Viironen & Poutanen (2004)

  10. Synthetic MSP X-ray pulse profiles - R = 10km, M = 1.4 M - Teff = 2  106 K (H atmosphere) - 2 antipodal, point-like polar caps Bogdanov, Grindlay, & Rybicki (2008)

  11. Gravitational redshift & bending of photon trajectories Schwarzschild Flat Nollert et al. (1989) For M = 1.4 M, R = 10 km ~80% of the entire neutron star surface is visible at a given instant.

  12. Model MSP X-ray pulse profiles: Constraints on the NS EOS } 9 km 12 km 16 km for M = 1.4 M =10°, =30° =30°, =60° * Fits to X-ray pulse profiles of MSPs can be used to infer NS compactness 1 + zg = (1 – 2GM/c2R)–1/2(Pavlov & Zavlin 1997; Zavlin & Pavlov 1998) * Independent mass measurement for binary MSPs (e.g. PSR J04374715, M=1.76  0.2 M)  constrain R separately  tight constraint on NS EOS =60°, =80° =20°, =80° Bogdanov et al. (2007, 2008)

  13. Neutron Star Hydrogen Atmosphere Model • Unmagnetized (B108 G ~ 0), Optically-Thick Hydrogen Atmosphere: - 100% pure hydrogen due to gravitational sedimentation - harder than blackbody for same effective temperature - energy-dependent limb darkening } Zavlin et al. (1996) cos=0 BB H atm. cos=103 Courtesy of G.B. Rybicki

  14. Model MSP X-ray pulse profiles: H atmosphere vs blackbody - P = 4ms, R = 10 km, M = 1.4 M - Teff = 2  106 K (H atmosphere) - 2 antipodal, point-like polar caps =10°, =30° Blackbody Blackbody + Doppler H atmosphere H atmospere + Doppler =30°, =60° Due to limb-darkening, H atmosphere pulse profiles differ substantially from Blackbody and are required =60°, =80° =20°, =80° (see Pavlov & Zavlin 1997; Zavlin & Pavlov 1998; Bogdanov et al. 2007, 2008) Bogdanov et al. (2007)

  15. PSR J0437–4715 (nearest and brightest MSP) P = 5.757451924362137(99) ms D = 156.3  1.3 pc LX = 3  1030 ergs s–1 M = 1.76  0.2 M NH = 2  1019 cm–2 XMM–Newton EPIC-pn fast timing mode 0.3–2 keV 69 ks Black body H-atmos Bogdanov, Rybicki, & Grindlay (2007)

  16. Two-temperature H atmosphere T1 2 × 106 K T2  0.5 × 106 K R1  300 m R2 2 km Inconsistent with blackbody H atmosphere + centered dipole Offset dipole required (~1 km) PSR J0437–4715 69 ks R = 8.5–17.6 km (95% confidence) R measured since R > 8.5 km (99.9% confidence) for M = 1.76 M Bogdanov, Rybicki, & Grindlay (2007)

  17. PSR J0030+0451 Nearby (D  300 pc) isolated MSP Two-temperature H atmosphere T1 1.5 × 106 K T2  0.7 × 106 K R1  400 m R2 1.5 km Inconsistent with blackbody H atmosphere required Evidence for offset dipole XMM–Newton EPIC pn 130 ks R > 10.6 km (95% conf.) R > 10.4 km (99.9% conf.) Lower limits since angles α, ζnot fixed for M = 1.4 M Bogdanov & Grindlay in prep.

  18. Constraints on M/R for MSP J0030+0451 95% conf. limits: For M ≥1.4Msun R ≥ 10.6km Rules out Quark Star models SQM1, SQM3 (Bogdanov & Grindlay 2009)

  19. Modeling Thermal X-ray Emission from MSPs • Most (?) Promising method for constraints on NS EOS: • Extraordinary rotational stability (P =5.757451924362137(99) for J04374715) • Non-transient (always “on”) and non-variable • “Weak” magnetic fields (Bsurf~108–9 G) B-field does not affect radiative properties of atmosphere • Dominant thermal emission(95% of total counts @ 0.1–2 keV) • Radiation from small fraction of NS surface(Reff  2 km)  emission region size and shape only important at 1% level • High precision distances(0.8% for PSR J04374715; Deller et al. 2008)  uncertainty in (Reff/D)2 greatly reduced • Independent, accurate mass measurements possible from radio timing unique constraint on R

  20. Conclusions • Bursts involve time-variable phenomena; not ideal but provide interesting constraints on M/R • qLMXBs in “purely thermal” state (without complications of hard-emission components found from PWN and/or propeller effect contributions) give more reliable M/R • MSPs with thermal polar cap emission offer best M/R constraints • MSP J0437-4715 is a clean (WD-NS) binary. Shapiro delay timing will give M; angles α, ζ can be measured. Actual values of M and R can/will be obtained !

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