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The Neutron Star Equation of State- Electromagnetic Observations

The Neutron Star Equation of State- Electromagnetic Observations. Frits Paerels Columbia University GWPAW, UW Milwaukee, January 26, 2011. Planets: an Analogy. Measurements of mass and radius. Model M-R relation, based on Equation of State. Courtesy Dimitar Sasselov /Harvard

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The Neutron Star Equation of State- Electromagnetic Observations

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  1. The Neutron Star Equation of State-Electromagnetic Observations Frits Paerels Columbia University GWPAW, UW Milwaukee, January 26, 2011

  2. Planets: an Analogy Measurements of mass and radius Model M-R relation, based on Equation of State Courtesy DimitarSasselov/Harvard Nature, 2008

  3. Phase Diagram of H2O Courtesy DimitarSasselov

  4. Neutron Star Masses single/double-lined binaries + optical vradspectroscopy of distorted star Black Widow: MPSR = 2.40 ± 0.12 MO single/double-lined binaries + relativistic effects single-lined binaries + relativistic effects J1614-2230: MNS = 1.97 ± 0.04 MO Diagram from Lattimer&Prakash‘What a Two Solar Mass Neutron Star Really Means’, 1012.3208v1

  5. J1614-2230: PSR + WD,i= 89°.17 (!!) spectacular Shapiro delay: clean mass measurement (*) WD is point mass DeMorest, Pennucci, Ransom, Roberts, Hessels, Nature, 467, 1083 (2010)

  6. Neutron Star Radii

  7. Neutron Star Radius radio: X (radio emission not associated with NS surface) If ~ blackbody: optical: T = 5800 K, R = 10 km: MV 24 mag fainter than Sun; at 100 pc: mV = 4.82 + 24 + 5 = 33.8 … T = 106 K: gain 22 magnitudes; a few NS can be seen If hotter, will be an X-ray source: X-ray: Emax ~ 250 eV (T/106 K); L ~ LEdd for T ~ 107 K (for 1MO)

  8. RXJ1856.5-3754: indeed, sort of like a blackbody (kT ~ 60 eV) Chandra LETGS: Drake et al., Ap.J., 572, 996 (2002)

  9. Measuring the Mass and the Radius • Absolute Photometry: fν/Fν= (R/D)2 ; need Fν(Teff, log g, composition, B, …) • Need the distance D! • Also need to know what fraction of the stellar surface radiates! • The Magnificent Seven: seven soft X-ray sources with a ‘stellar’ spectrum and a • distance estimate from Kaplan: 0801.1143

  10. The interpretation of the photospheric spectrum is non-trivial: from Kaplan: 0801.1143 Other attractive idea: use neutron stars in Globular Clusters (known D)

  11. 2. X-ray Burst Sources: go up to LEdd for 10 seconds, at T ~ 107 K Photospheric emission easily detectable. If D known: same as previous. 3. Periodically variable (spinning) X-ray bursters (‘hot spot’): combine spin period, Doppler shift; plus GR effects (lensing) on pulse shape: mass AND radius! Currently, constrains (1 – RS/R)1/2 ; in future, M and R. Burst oscillations in EXO0748-676 Galloway et al., Ap.J.(Letters), 711, L148 (2010)

  12. 4. PhotosphericSpectroscopy Most sensitive way to measure parameters: absorption line spectroscopy a replay of classical stellar spectroscopy, with strong twists! Ongoing accretion ensures ~ solar abundances Expect: metals highly ionized, so focus on Fe Line profiles sensitive to Doppler broadening, lensing, Lense-Thirring, … Spin frequency 400 Hz Full stellar surface R/M = 4.82 G/c2 Özel and Psaltis, Ap.J.(Letters), 582, L31 (2003)

  13. Line Profiles and Equivalent Widths Doppler broadening of Fe: v/c = (kT/Mc2)1/2 = 1.3 x 10-4 (T/107 K)1/2 Absorption lines saturate, very hard to detect unless spectroscopic resolving power > 5000 (NB. Stellar rotation does not affect [increase] the line contrast) Easy to show that Stark broadening should easily be detectable: ΔE ~ pE~ (a0 e/Z) (e/r2) ~ n2/3 ~ g2/3 which is sensitive to density, hence to gravity! Combine gravitational redshift with g, get M and R. In practice, bursters spin rapidly, so cannot be done with current instruments

  14. Baryonic EoS So how far along are we? typical, somewhat model- dependent M/R constraint from X-ray observations Hyperons, ‘Exotic’ condensates From Demorest et al., 2010 Free Quarks

  15. Other techniques: Precession of NS spin axis in binary: constrains moment of inertia I PSR 0737-3039 A+B: binary pulsar, known masses; geodetic precession of S around L with 71/75-yr period; LS coupling introduces additional periastron advance Hypothetical: 10% accuracy on I Lattimer&Prakash: Phys.Reports, 2007

  16. Prospects: spin-phase resolved photospheric spectroscopy with the International X-ray Observatory IXO Fe XXVI Hα Fe XXVI Lyα And this will be multiply-redundant in M and R (also get redshift and g !)

  17. XMM/RGS: Cumulative spectrum of 30 X-ray bursts If correct identification: gravitational redshift! z = 0.35 (Cottam, Paerels, & Mendez, 2002, Nature, 420, 51)

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