The Neutron Star Equation of State-Electromagnetic Observations

Frits PaerelsColumbia University

GWPAW, UW Milwaukee, January 26, 2011

Courtesy Dimitar Sasselov/HarvardNature, 2008

Measurements of mass and radius

Model M-R relation, based on Equation of State

Planets: an Analogy

Phase Diagram of H2O

Courtesy Dimitar Sasselov

Neutron Star Masses

single/double-lined binaries + relativistic effects

single/double-lined binaries

+ optical vrad spectroscopyof distorted star

Diagram from Lattimer&Prakash ‘What a Two Solar Mass Neutron Star Really Means’, 1012.3208v1

single-lined binaries + relativistic effects

J1614-2230:MNS = 1.97 ± 0.04 MO

Black Widow:MPSR = 2.40 ± 0.12 MO

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

Neutron Star Radii

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)

RX J1856.5-3754: indeed, sort of like a blackbody (kT ~ 60 eV)

Chandra LETGS: Drake et al., Ap.J., 572, 996 (2002)

Measuring the Mass and the Radius1. 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

from Kaplan: 0801.1143

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 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.

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4. Photospheric Spectroscopy

Most sensitive way to measure parameters: absorption line spectroscopya replay of classical stellar spectroscopy, with strong twists!

Ongoing accretion ensures ~ solar abundancesExpect: 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 HzFull stellar surfaceR/M = 4.82 G/c2

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 ~ pE ~ (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

From Demorest et al., 2010

So how far along are we?Baryonic EoS

Hyperons,‘Exotic’ condensatesFree Quarks

typical,somewhat model-dependentM/R constraintfrom X-rayobservations

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

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