The Radius of Neutron Stars

Transcription

1 The Radius of Neutron Stars Bob Rutledge McGill University Collaborators: Sebastien Guillot (McGill). Mathieu Servillat (Saclay) Natalie Webb (Toulouse). Ed Brown (MSU) Lars Bildsten (UCSB/KITP) George Pavlov (PSU) Vyacheslav Zavlin (MSFC).

2 A physicist, in 203, cannot solve equations which permit an analytic prediction from the physics of the strong force regarding the systems where this force is important: the properties and behavior of matter at and above nuclear density. This can be done for gravitation, the weak force, and electromagnetic forces. This is a major hole in modern physics.

3 The Dense Matter Equation of State is an important Strong Force Regime Each different proposed deos produces a different massradius relationship for neutron stars. 5% Accuracy Thus, measure the massradius relationship of neutron stars, and you have a measurement of the deos. Precision requirement -- 5% in mass and radius, separately. A larger uncertainty is useless to nuclear physics. Lattimer et al

4 Mass-Radius Relation from the Equation of State Measuring the Mass and Radius simultaneously is difficult. Lattimer & Prakash (2000) High-mass measurements prefer EOSs which produce a nearly constant radius at astrophysically interesting masses. PSR J0348 (Antoniadis et al 203) PSR J64 (Demorest et al 200) Precision Radius Measurements (<5%) may be they key to measuring the deos.

5 Neutron Star Structure: The Cartoon Picture Atmosphere Envelope Crust Outer Core Inner Core Credit: Dany Page

6 Estimated Equations of State Different calculational (approximation) methods Different input physics Different nuclear parameters (example: nuclear compressibility as a function of fractional neutron excess). Lattimer and Prakash (2000)

7 From Neutron Star Mass-Radius Relation to the Equation of State P = f( ) Lindblom (992) showed that each Dense Matter Equation of State maps to a unique Mass-Radius relationship for neutron stars. Ozel and Psaltis (2009) demonstrate how to perform the inverse problem: take the mass-radius relationship, and produce an equation of state. Only ~5-7 such objects are needed, but with different masses, to derive a new dense matter equation of state. Thus, measurement of the neutron star mass-radius relationship would implicate a unique deos. Short Course: Gravity pulls inward Pressure Pushes Outward Result: R=f(M) F g M(< R)

8 Timing measurements -- which permit NS mass measurements -- are limited in precision by the stability of rotation in NS (very high) and the precision of the comparison clocks (very high). Pulsars VERY LOW SYSTEMATIC UNCERTAINTIES Result: Masses are measured to 0.000%

9 Quiescent Low Mass e X-ray Binaries (qlmxb) Companion Star Composition: 75% H 23% He 2% other Outburst X-ray image (in quiescence) Optical image (in outburst) Quiescence Optical image (in outburst) Transient LMXBs in quiescence are H atmosphere neutron stars, powered by a core heated through equilibrium nuclear reactions in the crust. Brown, Bildsten & RR (998)

10 Gravity qlmxbs, in this scenario, have pure Hydrogen atmospheres When accretion stops, the He (and heavier elements, gravitationally settle on a timescale of ~0s of seconds (like rocks in water), leaving the photosphere to be pure Hydrogen (Alcock & Illarionov 980, Bildsten et al 992). H Photosphere He Brown, Bildsten & RR (998)

11 Emergent Spectrum of a Neutron Star Hydrogen Atmosphere H atmosphere calculated Spectra are ab initio radiative transfer calculations using the Eddington equations. Zavlin, Pavlov and Shibanov(996) - NSA Rajagopal and Romani (996); Zavlin et al (996); Pons et al (2002; Heinke et al (2006) -- NSATMOS; Gaensicke, Braje & Romani (200); Haakonsen et al (202) All comparisons show consistency within ~few % (e.g. Webb et al 2007, Haakonsen 202). Vetted : X-ray spectra of Zavlin, Heinke together have been used in several dozen works. 4 R F = 4πT eff, D R = R 2GM c 2 R 2 RR et al (999,2000)

12 ρ (g cm -3 ) Begi Non-Equilibrium Processes in the Outer Crust inning with 56 Fe (Haensel &Zdunik 990, 2003) Reaction Δρ ρ Q (Mev/np) Fe 56 Cr - 2e- + 2ν e Cr 56 Ti - 2e- + 2ν e Ti 56 Ca - 2e- + 2ν e Ca 56 Ar - 2e- + 2ν e Ar 52 S +4n - 2e- + 2ν e Non-Equilibrium Processes in the Inner Crust ρ (g cm -3) Reaction X Q n (Mev/np) S 46 Si +6n - 2e- + 2ν e Si 40 Mg + 6n - 2e- + 2ν e Deep Crustal Heating Begins Here Ends Here Mg 34 Ne + 6n - 2e- + 2ν e 34 Ne+ 34 Ne 68 Ca Ca 62 Ar +6n - 2e- + 2ν e Ar 56 S + 6n - 2e- + 2ν e S 50 Si + 6n - 2e- + 2ν e Si 44 Mg + 6n - 2e- + 2ν e Mg 36 Ne + 6n - 2e- + 2ν e 36 Ne+ 36 Ne 72 Ca 68 Ca 62 Ar + 6n - 2e- + 2ν e Ar 60 S + 6n - 2e- + 2ν e S 54 Si + 6n - 2e- + 2ν e Si 48 Mg + 6n - 2e- + 2ν e Mg+ 48 Mg 96 Cr Cr 88 Ti + 8n - 2e- + 2ν e Mev per np Brown, Bildsten & RR (998)

13 Assumptions -- the systematic uncertainties. H atmosphere neutron stars. Expected from a Hydrogen companion LMXB; can be supported through optical observations of a H companion. Low B-field (<0 0 G) neutron stars. This is true for standard LMXBs as a class, but difficult to prove on a case-by-case basis. Emitting isotropically. Occurs naturally when powered by a hot core. Non-Rotating neutron stars. qlmxbs are observed to rotate at Hz. This can be a significant fraction of the speed of light. Doppler boosting and deviation from NS spheroidal geometry are not included in emission models. These effects should be calculated, but have not yet been. If you don t like these assumptions: We find the assumptions not strongly supported and therefore ignore this result.

14 Instruments for measurements of qlmxbs Chandra X-ray Observatory Launched 999 (NASA) resolution XMM/Newton Launched 999 (ESA) 6 resolution ~4x area of Chandra. Every photon is time tagged (~ sec), with its energy measured (E/deltaE = 0) with full resolution imaging.

15 Aql X- with Chandra -- Field Source X-ray Absorption (α p =) F pl =5% (0.5-0 kev) RR et al (200b) R (d/5 kpc) kt eff, (e20 cm -2 ) N H km ev 35 7

16 The LMXB Factories: Globular Clusters GCs : overproduce LMXBs by 000x vs. field stars Many have accurate distances measured. NGC D (kpc) +/-(%) qlmxbs can be identified by their soft X-ray spectra, and confirmed with optical counterparts Carretta et al (2000)

17 NGC 539 (Omega Cen) qlmxbs can be identified by their soft X-ray spectra, and confirmed with optical counterparts. Rc=56.7Rc The identified optical counterpart demonstrates unequivocally the X-ray source is a qlmxb. An X-ray source well outside the cluster core Spitzer (Infrared)

18 NGC 539 (Omega Cen) X-ray Spectrum is inconsistent with any other type of known GC source (pulsars, CVs, coronal sources). Full confirmation as LMXB requires Hubble photometry R (d/5 kpc) kt eff, (e20 cm -2 ) N H 4.3 ± 2. km ev (9) RR et al (2002)

19 All qlmxbs used in this work were previously identified and analysed, with resulting R published. Name kt_eff(infty) (ev) NH Fx (0-3 cgsflux) Band (kev) Ref. R(infty) 47 Tuc X7 05(5) 0.04(2) Heinke et al (2006) <: 5 47 Tuc X5 00(20) 0.09(7) Heinke et al (2003) < 5 M28 90(+30-0) 0.26(4) Becker et al (2003) <5 NGC 6304 X9 5(20) [0.266] Guillot et al (2009) NGC 6304 X4 20(20) [0.266] Guillot et al (2009) +++ <5 NGC 6397 (U24) 74(8) Grindlay et al (200 < 5 M3 76(3) [0.0] Gendre et al (2003) DONE NGC 320 X6 70 (50) [0.4] Webb et al (2006) Data taken NGC 6553 X9 00 (20) [0.35] Guillot et al (in prep) +++ Omega Cen 67(2) 0.09(3) Rutledge et al (2002), Gendre et al (2003) NGC 6637 X3 00 (40) [0.] Guillot et al (in prep) +++ M30 A- 94(5) 0.03() Lugger (2007) NGC 6553 X3 27(+7-45) [0.35] Guillot et al (in prep) <: 5 DONE <0 NGC 6304 X5 70(25) [0.266] Guillot et al (2008) +++ NGC 6553 x35 88 (60) [0.35] Guillot et al (in prep) +++ NGC 2808 C Servillat et al (2008) <5 M80 CX2 82(2) 0.09(2) Heinke et al (2003) <5 M80 CX6 76(6) 0.22(7) Heinke et al (2003) <5

20 Measuring the Radius of Neutron Stars from qlmxbs in Globular Clusters The 2.0 solar mass neutron stars favor hadronic deoss over quark and phasetransition deoss. These have the property of a quasi-constant neutron star radius. Analysis goal: Using all suitable qlmxb X- ray data sets of targets (there are five) provide the most reliable neutron star radius measurement possible. Assume the radius of neutron stars is quasi-constant (a constant, at astrophysically important masses, within measurement error). Perform a Markoff-Chain-Monte-Carlo (MCMC) and include all known uncertainties and use conservative assumptions.

21 All previous EoS work treated measurements of each NS independently, and combined their statistics = Source Source 2 R M T NH, R2 M2 T2 NH,2 0 2 a,2 a,3 a, R R a 2, 2 a 2,3 a 2, M M a 3, a 3,2 2 a 3, T T a 4, a 4,2 a 4, N H NH, a 5,6 a 5,7 a 5,8 R 2 R a 6,5 2 a 6,7 a 6,8 M 2 M a 7,5 a 7,6 2 a 7,8 C T 2 A T a 8,5 a 8,6 a 8,7 2 N H2 NH,2 T Increase M increase R increase Absorption Increase

22 Joint Fits - the major difference from previous = Source Source 2 0 R M T NH, R M2 T2 NH,2 2 a,2 a,3 a,4 2 a,6 a,7 a,8 R R a 2, 2 a 2,3 a 2,4 a 2,5 2 a 2,7 a 2,8 M M,M 2 a 3, a 3,2 2 a 3,4 a 3,5 a 3,6 2 a 3,8 T T,T 2 a 4, a 4,2 a 4,3 2 a 4,5 a 4,6 a 4,7 2 N H 2 a 5,2 a 5,3 a 5,4 2 a 5,6 a 5,7 a 5,8 R R a 6, 2 a 6,3 a 6,4 a 6,5 2 a 6,7 a 6,8 M 2,M M 2 7, a 7,2 2 a 7,4 a 7,5 a 7,6 2 a 7,8 T 2,T T 2 a 8, a 8,2 a 8,3 2 a 8,5 a 8,6 a 8,7 2 N H2,N H N H,N H2 Every parameter (M, R, T, N_H) of all five sources affects every other parameter of every source N H2 C A R M T NH, R2 M2 T2 NH,2 S N / N 2 (# of Source Matrix Elements) N(# of sources) = N In comparison to using the sources independently, its as if we have 25 sources, instead of 5 sources.

23 Best H atmosphere (+ PL) spectral fit of all 5 qlmxbs This model is a statistically acceptable fit to the X-ray spectral data. This is an a posteriori confirmation that the data are consistent with our assumptions. After finding the best fit a MCMC method was used to find the uncertainty regions for all parameters - -- the Radius, Mass, Temperature, absorption, distance, and power-law normalization. 2 /dof = 0.98/628(prob. = 0.64) Guillot et al (203)

24 NH free, D gaussian bayesian priors, PL included. Guillot et al (203)

25 The Neutron Star Radius < km (99% conf) km (90%conf.) M-R by J. Lattimer WFF= Wiring, Fiks and Fabrocini (988) Guillot et al (203) Contains uncertainties from: Distance All spectral parameters Calibration