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The Neutron Star Equation of State- Electromagnetic Observations Frits Paerels Columbia University GWPAW, UW Milwaukee, January 26, 2011
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Courtesy Dimitar Sasselov/Harvard Nature, 2008 Measurements of mass and radius Model M-R relation, based on Equation of State Planets: an Analogy
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Phase Diagram of H 2 O Courtesy Dimitar Sasselov
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Neutron Star Masses single/double-lined binaries + relativistic effects single/double-lined binaries + optical v rad spectroscopy of distorted star Diagram from Lattimer&Prakash ‘What a Two Solar Mass Neutron Star Really Means’, 1012.3208v1 single-lined binaries + relativistic effects J1614-2230: M NS = 1.97 ± 0.04 M O Black Widow: M PSR = 2.40 ± 0.12 M O
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DeMorest, Pennucci, Ransom, Roberts, Hessels, Nature, 467, 1083 (2010) J1614-2230: PSR + WD, i = 89 °.17 (!!) spectacular Shapiro delay: clean mass measurement (*) WD is point mass
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Neutron Star Radii
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Neutron Star Radius radio: X (radio emission not associated with NS surface) If ~ blackbody: optical: T = 5800 K, R = 10 km: M V 24 mag fainter than Sun; at 100 pc: m V = 4.82 + 24 + 5 = 33.8 … T = 10 6 K: gain 22 magnitudes; a few NS can be seen If hotter, will be an X-ray source: X-ray: E max ~ 250 eV (T/10 6 K); L ~ L Edd for T ~ 10 7 K (for 1M O )
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RX J1856.5-3754: indeed, sort of like a blackbody (kT ~ 60 eV) Chandra LETGS: Drake et al., Ap.J., 572, 996 (2002)
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Measuring the Mass and the Radius 1.Absolute Photometry: f ν /F ν = (R/D) 2 ; need F ν (T eff, 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
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The interpretation of the photospheric spectrum is non-trivial: Other attractive idea: use neutron stars in Globular Clusters (known D)
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2. X-ray Burst Sources: go up to L Edd for 10 seconds, at T ~ 10 7 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 – R S /R) 1/2 ; in future, M and R. Burst oscillations in EXO0748-676 Galloway et al., Ap.J.(Letters), 711, L148 (2010)
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4. Photospheric Spectroscopy 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, … Özel and Psaltis, Ap.J.(Letters), 582, L31 (2003) Spin frequency 400 Hz Full stellar surface R/M = 4.82 G/c 2
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Line Profiles and Equivalent Widths Doppler broadening of Fe: v/c = (kT/Mc 2 ) 1/2 = 1.3 x 10 -4 (T/10 7 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 ~ (a 0 e/Z) (e/r 2 ) ~ n 2/3 ~ g 2/3 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
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From Demorest et al., 2010 So how far along are we? Baryonic EoS Hyperons, ‘Exotic’ condensates Free Quarks typical, somewhat model- dependent M/R constraint from X-ray observations
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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 Lattimer&Prakash: Phys.Reports, 2007 Hypothetical: 10% accuracy on I
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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 !)
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XMM/RGS: Cumulative spectrum of 30 X-ray bursts (Cottam, Paerels, & Mendez, 2002, Nature, 420, 51) If correct identification: gravitational redshift! z = 0.35
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