1 / 17

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

mira
Download Presentation

The Neutron Star Equation of State- Electromagnetic Observations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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)

More Related