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

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

Phase Diagram of H 2 O Courtesy Dimitar Sasselov

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’, v1 single-lined binaries + relativistic effects J : M NS = 1.97 ± 0.04 M O Black Widow: M PSR = 2.40 ± 0.12 M O

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

Neutron Star Radii

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 = = 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 )

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

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:

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

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 EXO Galloway et al., Ap.J.(Letters), 711, L148 (2010)

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

Line Profiles and Equivalent Widths Doppler broadening of Fe: v/c = (kT/Mc 2 ) 1/2 = 1.3 x (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

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

Other techniques: Precession of NS spin axis in binary: constrains moment of inertia I PSR 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

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 !)

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